Interpreting box plots

WEBVTT
Kind: captions
Language: en

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- [Voiceover] So i have
a box and whiskers plot

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showing us the ages of
students at a party.

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And what I'm hoping to do in this video is

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get a little bit of
practice interpreting this.

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And what I have here are
five different statements

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and I want you to look
at these statements.

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Pause the video, look at these statements,

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and think about which of these,

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based on the information in
the box and whiskers plot,

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which of these are for sure true,

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which of these are for sure false,

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and which of these we don't
have enough information,

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it could go either way.

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Alright, so let's work through these.

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So the first statement is
that all of the students

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are less than 17 years old.

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Well we see, right over
here, that the maximum age,

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that's the right end of
this right whisker is 16.

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So it is the case that
all of the students are

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less than 17 years old.

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So this is definitely going to be true.

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The next statement.

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At least 75% of the students
are 10 years old or older.

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So, when you look at
this, this feels right,

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because 10 is, 10 is the value

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that is at the beginning
of the second quartile.

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This is the second
quartile right over there.

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And actually, let me do this,

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let me do this in a different color.

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So, this is the second quartile.

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So 25% of the value of the
numbers are in the second,

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or roughly, sometimes it's not exactly,

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so approximately, I'll say roughly 25%

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are going to be in this second quartile,

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approximately 25% are going
to be in the third quartile,

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and approximately 25% are going to

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be in the fourth quartile.

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So it seems reasonable for
saying 10 years old or older

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that this is going to be,

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this is going to be true.

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In fact, you could even have a couple

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of values in the first
quartile that are 10.

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But to make that a little more tangible,

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let's look at some, so I'm feeling,

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I'm feeling good that this is true,

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but let's look a few more examples

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to make this a little more concrete.

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So they don't know, we don't know,

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based on the information here exactly

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how many students are at the party.

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We'll have to construct some scenarios.

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So we could do a scenario,

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let's see if we can do...

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We could do a scenario where

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well let's see, let's see if I can,

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I can construct something
where, let's see,

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the median is 13.

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We know that for sure.

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The median is 13, so if
I have an odd number,

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I would have 13 in the
middle, just like that,

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and maybe I have three on either side.

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And I'm just making that number up.

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I'm just trying to see what I can learn

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about different types of data sets

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that could be described by
this box and whiskers plot.

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So 10 is going to be the
middle of the bottom half.

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So that's 10 right over there.

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And 15 is going to be the
middle of the top half.

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That's what this box and
whiskers plot is telling us.

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And they of course tell
us what the minimum,

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the minimum is seven.

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And they tell us that the maximum is 16.

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So we know that's seven
and then that is 16.

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And then this, right over
here, could be anything.

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It could be 10, it could be 11,

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it could be 12, it could be 13.

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It wouldn't change what these medians are.

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It wouldn't change this
box and whiskers plot.

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Similarly, this could
be 13, it could be 14,

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it could be 15, and so any of those

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values wouldn't change it.

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And so 75% are 10 or older, well,

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this value, in this case, six out of seven

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are 10 years old or older.

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And we could try it out with other,

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other scenarios where...

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let's try to minimize the number
of 10s given this data set.

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Well we could do something like,

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let's say that we have eight.

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So let's see, one, two, three, four,

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five, six, seven, eight.

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And so here we know that the minimum,

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we know that the minimum is seven,

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we know that the maximum is 16.

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We know, we know that the,

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we know that the mean of
these middle two values,

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we have an even number now so,

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the median is going to be
the mean of these two values.

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So, it's going to be the
mean of this and this,

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is going to be 13.

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And we know that the mean of,

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we know that the mean of this and this

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is going to be 10 and that
the mean of this and this

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is going to be, is going to be 15.

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So what could we construct?

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Well actually, we don't
even have to construct

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to answer this question.

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We know that, we know that this is going,

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this is going to have to be 10 or larger.

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And then all of these other things

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are going to be 10 or larger,
so this is exactly 75%.

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Exactly 75% if we assume
that this is less than 10,

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are going to be 10 years old or older.

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So feeling very good, very good,

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about this one right over here.

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And actually, just to make this concrete,

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I'll put in some values here.

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You know this could be,

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this could be a nine and an 11.

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This could be a 12 and a 14.

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This could be a 14 and a 16.

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Or, it could be, it
could be a 15 and a 15.

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You could think about
it and in any of those,

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in any of those ways.

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But feeling very good
that this is definitely

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going to be true based on the information

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given in this plot.

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Now they say there's only one
seven-year-old at the party.

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One seven-year-old at the party.

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Well this first, this first
possibility that we looked at,

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that was the case.

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There was only one
seven-year-old at the party

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and there was one
16-year-old at the party.

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And actually, that was the next statement,

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there's only one 16-year-old at the party.

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So both of these seem like we can

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definitely construct
data that's consistent

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with this box plot, box and whiskers plot,

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where this is true.

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But could we construct
one where it's not true?

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Well sure.

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Let's imagine, let's see,
we have our median at 13.

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Median at 13.

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And then we have, let's see,

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one, two, three, four, five.

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One, two, three, four, five.

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This is gonna be, this is gonna be the 10,

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the median of this bottom half.

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This is going to be 15.

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This is going to be seven.

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This is going to be 16.

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Well this could also be seven.

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It doesn't have to be.

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It could be seven, eight, nine, or ten.

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This could also be 16.

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Doesn't have to be.

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It could be 15 as well.

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But just like that, I've
constructed a data set,

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and these could be, you know
this could be 10, 11, 12, 13.

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This could be 10, 11, 12, 13.

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This could be 13, 14, 15.

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This one also could be 13, 14, 15.

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But the simple thing is,
or the basic idea here,

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I can have a data set where
I have multiple sevens

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and multiple 16s, or I
could have a data set

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where I only have one
seven or only one 16.

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So both of these statements,
we just plain don't know.

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We just don't, we just don't know.

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Now the next statement,

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exactly half the students
are older than 13.

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Well if you look at this
possibility up here,

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we saw that three out of the seven

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are older than 13.

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So that's not exactly half.

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3/7 is not 1/2.

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But in this one over here, we did see that

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exactly half are over, are older than 13.

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In fact, if you're saying exactly half...

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Well, in this one we're
saying that exactly half

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are older than 13.

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We have an even number right over here.

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And so it is exactly half.

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So it's possible that it's true,

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it's possible that it's not true

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based on the information given.

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We once again,

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we once again don't,

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we once again do not know.

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Anyway, hopefully you
found this interesting.

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This is, the whole point of me doing this

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is when you look at statistics,

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sometimes it's easy to kind of say,

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okay I think it roughly means that,

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and that's sometimes okay.

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But it's very important
to think about what types

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of actual statements you can make

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and what you can't make
and it's very important

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when you're looking at statistics to say,

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well you know what, I just don't know.

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That the data actually is not telling me

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that thing for sure.


Mean absolute deviation example

WEBVTT
Kind: captions
Language: en

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- This bar graph here tells us

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bubbles blown by each gum-chewer.

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We have four different gum-chewers,

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and they tell us how many
bubbles each of them blew.

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What I wanna do is, I
wanna figure out first

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the mean of the number of bubbles blown,

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and then also figure out
how dispersed is the data,

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how much do these vary from the mean.

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I'm gonna do that by calculating

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the mean absolute deviation.

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Pause this video now.

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Try to calculate the mean of
the number of bubbles blown.

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And then, after you do that, see if you

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can calculate the mean absolute deviation.

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Step one, let's figure out the mean.

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The mean is just going to be the sum

00:00:42.326 --> 00:00:44.442
of the number of bubbles blown

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divided by the number of datapoints.

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Manueala blew four bubbles.

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She blew four bubbles.

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Sophia blew five bubbles.

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Jada blew six bubbles.

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Tara blew one bubble.

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We have one, two, three, four datapoints.

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So let's divided by four.

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And so, this is going to be
equal to four plus five is nine,

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plus six is 15, plus one is 16.

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So it's equal to 16 over four,

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which is 16 divided by
four is equal to four.

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The mean number of bubbles blown is four.

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Lemme actually do this with
a bold line right over here.

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This is the mean number of bubbles blown.

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Now what I wanna do is I wanna figure out

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the mean absolute deviation.

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Mean.

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MAD: Mean Absolute Deviation.

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What we wanna do is we wanna
take the mean of how much

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do each of these datapoints
deviate from the mean.

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I know I just used the word
mean twice in a sentence,

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so it might be a little confusing,

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but as we work through it, hopefully,

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it'll make a little bit of sense.

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How much does Manueala's, the
number of bubbles she blew,

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how much does that deviate from the mean?

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Well, Manueala actually blew four bubbles,

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and four is the mean.

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So her deviation,

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her absolute deviation
from the mean is zero.

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Is zero.

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Actually, lemme just write this over here.

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Absolute deviation, that's AD,

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absolute deviation from the mean.

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Manueala didn't deviate
at all from the mean.

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Now let's think about Sophia.

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Sophia deviates by one from the mean.

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We see that right there, she's one above.

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Now, we would say one whether
it's one above or below,

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'cause we're saying absolute deviation.

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Sophia deviates by one.

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Her absolute deviation is one.

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And then, we have Jada.

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How much does she deviate from the mean?

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We see it right over here.

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She deviates by two.

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She is two more than the mean.

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And then, how much does
Tara deviate from the mean?

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She is at one, so that
is three below the mean.

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That is three below the mean.

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Once again, this is two, this is three.

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She deviates.

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Her absolute deviation is three.

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And then we wanna take the
mean of the absolute deviation.

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That's the M in MAD, in
Mean Absolute Deviation.

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This is Manueala's absolute deviation,

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Sophia's absolute deviation,
Jada's absolute deviation,

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Tara's absolute deviation.

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We want the mean of those,

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so we divide by the number of datapoints,

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and we get zero plus one,
plus two, plus three,

00:03:33.267 --> 00:03:34.970
is six over four.

00:03:34.970 --> 00:03:38.896
Six over four, which is
the same thing as 1 1/2.

00:03:38.896 --> 00:03:40.770
Or, lemme just write it
in all the different ways.

00:03:40.770 --> 00:03:44.937
We could write it as three
halves, or 1 1/2, or 1.5.

00:03:46.786 --> 00:03:48.943
Which gives us a measure of how much

00:03:48.943 --> 00:03:53.344
do these datapoints vary
from the mean of four.

00:03:53.344 --> 00:03:54.525
I know what some of you are thinking.

00:03:54.525 --> 00:03:55.988
"Wait, I thought there was a formula

00:03:55.988 --> 00:03:57.943
"associated with the
mean absolute deviation.

00:03:57.943 --> 00:03:59.205
"It seems really complex.

00:03:59.205 --> 00:04:01.034
"It has all of these absolute-value signs

00:04:01.034 --> 00:04:02.212
"and whatever else."

00:04:02.212 --> 00:04:04.018
That's all we did.

00:04:04.018 --> 00:04:05.824
When we write all those
absolute-value signs,

00:04:05.824 --> 00:04:08.260
that's just a fancy way of
looking at each datapoint,

00:04:08.260 --> 00:04:11.430
and thinking about how much
does it deviate from the mean,

00:04:11.430 --> 00:04:12.815
whether it's above or below.

00:04:12.815 --> 00:04:14.277
That's what the absolute value does.

00:04:14.277 --> 00:04:17.616
It doesn't matter, if it's
three below, we just say three.

00:04:17.616 --> 00:04:19.117
If it's two above, we just say two.

00:04:19.117 --> 00:04:21.635
We don't put a positive or negative on.

00:04:21.635 --> 00:04:23.326
Just so you're comfortable seeing how this

00:04:23.326 --> 00:04:26.050
is the exact same thing you
would've done with the formula,

00:04:26.050 --> 00:04:28.425
let's do it that way, as well.

00:04:28.425 --> 00:04:32.697
So the mean absolute deviation
is going to be equal to.

00:04:32.697 --> 00:04:35.152
Well, we'll start with Manueala.

00:04:35.152 --> 00:04:36.776
How many bubbles did she blow?

00:04:36.776 --> 00:04:38.159
She blew four.

00:04:38.159 --> 00:04:41.329
From that you subtract the mean of four,

00:04:41.329 --> 00:04:42.768
take the absolute value.

00:04:42.768 --> 00:04:44.522
That's her absolute deviation.

00:04:44.522 --> 00:04:48.344
Of course, this does evaluate
to this zero, to zero here.

00:04:48.344 --> 00:04:49.772
Then you take the absolute value.

00:04:49.772 --> 00:04:53.689
Sophia blew five bubbles,
and the mean is four.

00:04:54.551 --> 00:04:56.099
Then you do that for Jada.

00:04:56.099 --> 00:04:59.556
Jada blew six bubbles; the mean is four.

00:04:59.556 --> 00:05:01.630
And then you do it for Tara.

00:05:01.630 --> 00:05:05.213
Tara blew one bubble,
and the mean is four.

00:05:06.222 --> 00:05:09.396
Then you divide it by the
number of datapoints you have.

00:05:09.396 --> 00:05:11.103
Lemme make it very clear.

00:05:11.103 --> 00:05:14.354
This right over here,
this four, is the mean.

00:05:14.354 --> 00:05:15.532
This four is the mean.

00:05:15.532 --> 00:05:17.359
You're taking each of the datapoints,

00:05:17.359 --> 00:05:19.101
and you're seeing how far
it is away from the mean.

00:05:19.101 --> 00:05:20.421
You're taking the absolute
value 'cause you just

00:05:20.421 --> 00:05:23.039
wanna figure out the absolute distance.

00:05:23.039 --> 00:05:25.152
Now you see, or maybe you see.

00:05:25.152 --> 00:05:28.011
Four minus four, this is.

00:05:28.011 --> 00:05:28.844
Different color.

00:05:28.844 --> 00:05:30.548
Four minus four, that is a zero.

00:05:30.548 --> 00:05:33.231
That is that zero right over there.

00:05:33.231 --> 00:05:36.522
Five minus four, absolute value of that?

00:05:36.522 --> 00:05:37.882
That's going to be.

00:05:37.882 --> 00:05:39.908
Lemme do this in a new color.

00:05:39.908 --> 00:05:41.701
This is just going to be one.

00:05:41.701 --> 00:05:43.814
This thing is the same
thing as that over there.

00:05:43.814 --> 00:05:46.814
We were able to see
that just by inspecting

00:05:46.814 --> 00:05:48.833
this graph, or this chart.

00:05:48.833 --> 00:05:51.926
And then, six minus four,
absolute value of that,

00:05:51.926 --> 00:05:53.719
that's just going to be two.

00:05:53.719 --> 00:05:55.711
That two is that two right over here,

00:05:55.711 --> 00:05:58.477
which is the same thing as
this two right over there.

00:05:58.477 --> 00:06:02.011
And then, finally, our one
minus four, this negative three,

00:06:02.011 --> 00:06:04.687
but the absolute value of
that is just positive three,

00:06:04.687 --> 00:06:07.165
which is this positive
three right over there,

00:06:07.165 --> 00:06:10.280
which is this distance right over here.

00:06:10.280 --> 00:06:13.846
You divide it by four, you get 1.5 again.

00:06:13.846 --> 00:06:18.200
Hopefully you found this mean
absolute deviation example

00:06:18.200 --> 00:06:20.200
as interesting as I did.


Mean absolute deviation

WEBVTT
Kind: captions
Language: en

00:00:00.452 --> 00:00:01.234
- [Voiceover] Let's say that I've got

00:00:01.234 --> 00:00:02.701
two different data sets.

00:00:02.701 --> 00:00:05.804
The first data set, I have two,

00:00:05.804 --> 00:00:09.731
another two, a four, and a four.

00:00:09.731 --> 00:00:13.586
And then, in the other
data set, I have a one.

00:00:13.586 --> 00:00:15.741
We'll do this on the
right side of the screen.

00:00:15.741 --> 00:00:19.007
A one, a one, a six,

00:00:19.007 --> 00:00:21.175
and a four.

00:00:21.175 --> 00:00:22.877
Now, the first thing I
wanna think about is,

00:00:22.877 --> 00:00:23.733
"Well, how do I ...

00:00:23.733 --> 00:00:25.271
"Is there a number that can give me

00:00:27.348 --> 00:00:30.266
"a measure of center of
each of these data sets?"

00:00:30.266 --> 00:00:31.964
And one of the ways that
we know how to do that

00:00:31.964 --> 00:00:33.443
is by finding the mean.

00:00:33.443 --> 00:00:36.245
So let's figure out the mean
of each of these data sets.

00:00:36.245 --> 00:00:39.041
This first data set, the mean ...

00:00:39.041 --> 00:00:41.332
Well, we just need to sum
up all of the numbers.

00:00:41.332 --> 00:00:43.110
That's gonna be two plus two

00:00:43.110 --> 00:00:45.167
plus four plus four.

00:00:45.167 --> 00:00:45.910
And then we're gonna divide

00:00:45.910 --> 00:00:48.235
by the number of numbers that we have.

00:00:48.235 --> 00:00:50.866
So we have one, two, three, four numbers.

00:00:50.866 --> 00:00:52.578
That's that four right over there.

00:00:52.578 --> 00:00:55.443
And this is going to be,
two plus two is four,

00:00:55.443 --> 00:00:57.635
plus four is eight, plus four is 12.

00:00:57.635 --> 00:01:00.582
This is gonna be 12 over four,

00:01:02.474 --> 00:01:05.362
which is equal to three.

00:01:05.362 --> 00:01:07.478
Actually, let's see if
we can visualize this

00:01:07.478 --> 00:01:09.273
a little bit on a number line.

00:01:12.041 --> 00:01:13.411
Actually I'll do kind of a ...

00:01:13.411 --> 00:01:15.273
I'll do a little bit of a dot plot here

00:01:15.273 --> 00:01:17.203
so we can see all of the values.

00:01:18.346 --> 00:01:22.877
If this is zero, one, two,

00:01:22.877 --> 00:01:27.069
three, four, and five.

00:01:28.031 --> 00:01:29.436
We have two twos.

00:01:29.436 --> 00:01:30.677
Why don't I just do ...

00:01:30.677 --> 00:01:32.773
So for each of these twos ...

00:01:32.773 --> 00:01:34.371
Actually, I'll just do it in yellow.

00:01:34.371 --> 00:01:37.271
So I have one two, then
I have another two.

00:01:37.271 --> 00:01:38.610
I'm just gonna do a dot plot here.

00:01:38.610 --> 00:01:40.208
Then I have two fours.

00:01:40.208 --> 00:01:44.304
So, one four and another
four, right over there.

00:01:44.304 --> 00:01:46.809
And we calculated that the mean is three.

00:01:46.809 --> 00:01:48.447
The mean is three.

00:01:48.447 --> 00:01:50.866
A measure of central
tendency, it is three.

00:01:50.866 --> 00:01:52.410
So I'll just put three right over here.

00:01:52.410 --> 00:01:54.237
I'll just mark it with that dotted line.

00:01:54.237 --> 00:01:55.937
That's where the mean is.

00:01:55.937 --> 00:01:57.776
All right. Well, we've
visualized that a little bit.

00:01:57.776 --> 00:02:00.038
That does look like it's the center.

00:02:00.038 --> 00:02:01.870
It's a pretty ...

00:02:01.870 --> 00:02:03.040
It makes sense.

00:02:03.040 --> 00:02:05.557
So now let's look at this
other data set right over here.

00:02:06.603 --> 00:02:09.808
The mean, the mean over here

00:02:09.808 --> 00:02:12.542
is going to be equal to one plus one

00:02:12.542 --> 00:02:15.333
plus six plus four,

00:02:15.333 --> 00:02:17.908
all of that over, we still
have four data points.

00:02:17.908 --> 00:02:19.870
And this is two plus six is eight,

00:02:19.870 --> 00:02:21.352
plus four is 12,

00:02:21.352 --> 00:02:22.400
12 divided by four ...

00:02:22.400 --> 00:02:24.441
This is also three.

00:02:24.441 --> 00:02:26.279
So this also has the same mean.

00:02:26.279 --> 00:02:27.546
We have different numbers,

00:02:27.546 --> 00:02:30.433
but we have the same mean.

00:02:30.433 --> 00:02:32.044
But there's something about this data set

00:02:32.044 --> 00:02:33.906
that feels a little bit
different about this.

00:02:33.906 --> 00:02:35.266
And let's visualize it,

00:02:35.266 --> 00:02:36.970
to see if we can see a difference.

00:02:37.870 --> 00:02:39.970
Let's see if we can visualize it.

00:02:41.975 --> 00:02:43.870
I have to go all the way up to six.

00:02:43.870 --> 00:02:46.800
Let's say this is zero, one,

00:02:46.800 --> 00:02:50.733
two, three, four,

00:02:50.733 --> 00:02:52.668
five, six,

00:02:52.668 --> 00:02:54.725
and I'll go one more, seven.

00:02:54.725 --> 00:02:56.410
So we have a one.

00:02:56.410 --> 00:02:59.007
We have a one, we have another one.

00:03:00.345 --> 00:03:01.781
We have a six.

00:03:03.304 --> 00:03:04.868
And then we have a four.

00:03:05.546 --> 00:03:08.308
And we calculated that the mean is three.

00:03:08.308 --> 00:03:10.604
So we calculated that the mean is three.

00:03:10.604 --> 00:03:13.045
So the mean is three.

00:03:14.345 --> 00:03:15.797
When we measure it by the mean,

00:03:15.797 --> 00:03:18.840
the central point, or
measure of that central point

00:03:18.840 --> 00:03:20.009
which we use as the mean,

00:03:20.009 --> 00:03:22.966
well, it looks the same, but
the data sets look different.

00:03:22.971 --> 00:03:24.207
How do they look different?

00:03:24.207 --> 00:03:25.727
Well, we've talked about notions

00:03:25.727 --> 00:03:27.734
of variability or variation.

00:03:27.734 --> 00:03:30.745
And it looks like this data
set is more spread out.

00:03:30.745 --> 00:03:33.239
It looks like the data
points are on average

00:03:33.239 --> 00:03:34.941
further away from the mean

00:03:34.941 --> 00:03:37.010
than these data points are.

00:03:37.010 --> 00:03:38.371
That's an interesting question

00:03:38.371 --> 00:03:40.244
that we ask ourselves in statistics.

00:03:40.244 --> 00:03:43.841
We just don't want a measure
of center, like the mean.

00:03:43.841 --> 00:03:46.766
We might also want a
measure of variability.

00:03:46.766 --> 00:03:49.464
And one of the more straightforward ways

00:03:49.464 --> 00:03:51.038
to think about variability is,

00:03:51.038 --> 00:03:55.234
well, on average, how far
are each of the data points

00:03:55.234 --> 00:03:57.707
from the mean?

00:03:57.707 --> 00:03:58.977
That might sound a little complicated,

00:03:58.977 --> 00:04:00.533
but we're gonna figure out what that means

00:04:00.533 --> 00:04:03.865
in a second, (chortles) not
to overuse the word "mean."

00:04:03.865 --> 00:04:05.620
So we wanna figure out, on average,

00:04:05.620 --> 00:04:08.635
how far each of these
data points from the mean.

00:04:08.635 --> 00:04:09.900
And what we're about to calculate,

00:04:09.900 --> 00:04:14.205
this is called Mean Absolute Deviation.

00:04:14.210 --> 00:04:17.346
Absolute Deviation.

00:04:18.712 --> 00:04:20.206
Mean Absolute Deviation,

00:04:20.206 --> 00:04:22.700
or if you just use the acronym, MAD,

00:04:22.700 --> 00:04:26.014
mad, for Mean Absolute Deviation.

00:04:26.014 --> 00:04:26.900
And all we're talking about,

00:04:26.900 --> 00:04:29.267
we're gonna figure out how
much do each of these points,

00:04:29.267 --> 00:04:32.033
their distance, so absolute deviation.

00:04:32.033 --> 00:04:34.135
How much do the deviate from the mean,

00:04:34.135 --> 00:04:35.241
but the absolute of it?

00:04:35.241 --> 00:04:36.838
So each of these points at two,

00:04:36.838 --> 00:04:39.146
they are one away from the mean.

00:04:39.146 --> 00:04:40.513
Doesn't matter if they're less or more.

00:04:40.513 --> 00:04:42.122
They're one away from the mean.

00:04:42.122 --> 00:04:44.543
And then we find the mean
of all of the deviations.

00:04:44.543 --> 00:04:45.613
So what does that mean?

00:04:45.613 --> 00:04:47.642
(chuckles) I'm using the word "mean,"

00:04:47.642 --> 00:04:49.300
using it a little bit too much.

00:04:49.300 --> 00:04:51.307
So let's figure out the
Mean Absolute Deviation

00:04:51.307 --> 00:04:53.610
of this first data set.

00:04:53.610 --> 00:04:55.655
We've been able to figure
out what the mean is.

00:04:55.655 --> 00:04:57.366
The mean is three.

00:04:57.366 --> 00:04:59.271
So we take each of the data points

00:04:59.271 --> 00:05:00.536
and we figure out,

00:05:00.536 --> 00:05:03.624
what's its absolute
deviation from the mean?

00:05:03.624 --> 00:05:05.674
So we take the first two.

00:05:05.674 --> 00:05:08.867
So we say, two minus the mean.

00:05:08.867 --> 00:05:11.847
Two minus the mean, and we
take the absolute value.

00:05:11.847 --> 00:05:13.573
So that's its absolute deviation.

00:05:13.573 --> 00:05:15.311
Then we have another two,

00:05:15.311 --> 00:05:18.471
so we find that absolute
deviation from three.

00:05:18.471 --> 00:05:19.770
Remember, if we're just
taking two minus three,

00:05:19.770 --> 00:05:21.234
taking the absolute value,

00:05:21.234 --> 00:05:22.711
that's just saying its absolute deviation.

00:05:22.711 --> 00:05:24.381
How far is it from three?

00:05:24.381 --> 00:05:27.376
It's fairly easy to
calculate in this case.

00:05:27.376 --> 00:05:30.237
Then we have a four and another four.

00:05:31.143 --> 00:05:32.076
Let me write that.

00:05:32.076 --> 00:05:34.217
Then we have

00:05:34.217 --> 00:05:38.172
the absolute deviation of four from three,

00:05:38.172 --> 00:05:39.800
from the mean.

00:05:39.800 --> 00:05:41.669
Then plus, we have another four.

00:05:41.669 --> 00:05:43.976
We have this other four right up here.

00:05:43.976 --> 00:05:46.005
Four minus three.

00:05:46.005 --> 00:05:46.972
We take the absolute value,

00:05:46.972 --> 00:05:49.280
because once again,
it's absolute deviation.

00:05:49.280 --> 00:05:51.203
And then we divide it,

00:05:51.203 --> 00:05:53.833
and then we divide it by the
number of data points we have.

00:05:54.534 --> 00:05:55.937
So what is this going to be?

00:05:55.937 --> 00:05:57.912
Two minus three is negative one,

00:05:57.912 --> 00:05:59.279
but we take the absolute value.

00:05:59.279 --> 00:06:00.909
It's just going to be one.

00:06:00.909 --> 00:06:02.500
Two minus three is negative one.

00:06:02.500 --> 00:06:03.577
We take the absolute value.

00:06:03.577 --> 00:06:04.876
It's just gonna be one.

00:06:04.876 --> 00:06:05.934
And you see that here visually.

00:06:05.934 --> 00:06:08.309
This point is just one away.

00:06:08.309 --> 00:06:09.807
It's just one away from three.

00:06:09.807 --> 00:06:12.278
This point is just one away from three.

00:06:12.278 --> 00:06:13.798
Four minus three is one.

00:06:13.798 --> 00:06:15.444
Absolute value of that is one.

00:06:15.444 --> 00:06:18.187
This point is just one away from three.

00:06:18.187 --> 00:06:19.572
Four minus three, absolute value.

00:06:19.572 --> 00:06:21.006
That's another one.

00:06:21.006 --> 00:06:21.902
So you see in this case,

00:06:21.902 --> 00:06:25.140
every data point was exactly one away

00:06:25.140 --> 00:06:26.842
from the mean.

00:06:26.842 --> 00:06:27.671
And we took the absolute value

00:06:27.671 --> 00:06:29.072
so that we don't have negative ones here.

00:06:29.072 --> 00:06:33.116
We just care how far it
is in absolute terms.

00:06:33.116 --> 00:06:34.736
So you have four data points.

00:06:34.736 --> 00:06:37.579
Each of their absolute
deviations is four away.

00:06:37.579 --> 00:06:39.486
So the mean of the absolute deviations

00:06:39.486 --> 00:06:41.207
are one plus one plus one plus one,

00:06:41.207 --> 00:06:43.544
which is four, over four.

00:06:43.544 --> 00:06:45.073
So it's equal to one.

00:06:45.073 --> 00:06:46.667
One way to think about it is saying,

00:06:46.667 --> 00:06:50.137
on average, the mean of the
distances of these points

00:06:50.137 --> 00:06:53.283
away from the actual mean is one.

00:06:53.283 --> 00:06:54.797
And that makes sense because all of these

00:06:54.797 --> 00:06:58.337
are exactly one away from the mean.

00:06:58.337 --> 00:06:59.485
Now, let's see how,

00:06:59.485 --> 00:07:02.681
what results we get for this
data set right over here.

00:07:02.681 --> 00:07:03.835
And I'll do it ...

00:07:03.835 --> 00:07:05.854
Let me actually get some space over here.

00:07:05.854 --> 00:07:07.110
At any point, if you get inspired,

00:07:07.110 --> 00:07:08.175
I encourage you to calculate

00:07:08.175 --> 00:07:10.611
the Mean Absolute Deviation on your own.

00:07:10.611 --> 00:07:12.311
So let's calculate it.

00:07:12.311 --> 00:07:14.837
The Mean Absolute Deviation here,

00:07:14.837 --> 00:07:16.322
I'll write MAD,

00:07:16.322 --> 00:07:17.508
is going to be equal to ...

00:07:17.508 --> 00:07:18.989
Well, let's figure out
the absolute deviation

00:07:18.989 --> 00:07:21.530
of each of these points from the mean.

00:07:21.530 --> 00:07:23.807
It's the absolute value
of one minus three,

00:07:23.807 --> 00:07:25.380
that's this first one,

00:07:25.380 --> 00:07:27.341
plus the absolute deviation,

00:07:27.341 --> 00:07:29.977
so one minus three, that's the second one,

00:07:29.977 --> 00:07:32.416
then plus the absolute
value of six minus three,

00:07:32.416 --> 00:07:33.535
that's the six,

00:07:33.535 --> 00:07:34.378
then we have the four,

00:07:34.378 --> 00:07:36.733
plus the absolute value
of four minus three.

00:07:36.733 --> 00:07:39.585
Then we have four points.

00:07:39.585 --> 00:07:41.259
So one minus three is negative two.

00:07:41.259 --> 00:07:43.006
Absolute value is two.

00:07:43.006 --> 00:07:44.176
And we see that here.

00:07:44.176 --> 00:07:46.578
This is two away from three.

00:07:46.578 --> 00:07:48.376
We just care about absolute deviation.

00:07:48.376 --> 00:07:50.744
We don't care if it's to
the left or to the right.

00:07:50.744 --> 00:07:52.980
Then we have another one
minus three is negative two.

00:07:52.980 --> 00:07:55.111
It's absolute value, so this is two.

00:07:55.111 --> 00:07:58.283
That's this. This is
two away from the mean.

00:07:58.283 --> 00:07:59.731
Then we have six minus three.

00:07:59.731 --> 00:08:01.933
Absolute value of that
is going to be three.

00:08:01.933 --> 00:08:03.803
And that's this right over here.

00:08:03.803 --> 00:08:06.407
We see this six is three

00:08:06.407 --> 00:08:07.477
to the right of the mean.

00:08:07.477 --> 00:08:09.340
We don't care whether it's
to the right or the left.

00:08:09.340 --> 00:08:11.624
And then four minus three.

00:08:11.624 --> 00:08:14.711
Four minus three is one,
absolute value is one.

00:08:14.711 --> 00:08:15.398
And we see that.

00:08:15.398 --> 00:08:18.239
It is one to the right of three.

00:08:18.239 --> 00:08:19.271
And so what do we have?

00:08:19.271 --> 00:08:21.544
We have two plus two is four,

00:08:21.544 --> 00:08:24.218
plus three is seven, plus one is eight,

00:08:24.218 --> 00:08:27.534
over four, which is equal to two.

00:08:27.534 --> 00:08:30.157
So the Mean Absolute Deviation ...

00:08:30.157 --> 00:08:30.967
Let me write it down.

00:08:30.967 --> 00:08:32.341
It fell off over here.

00:08:32.341 --> 00:08:33.900
Here, for this data set,

00:08:33.900 --> 00:08:36.933
the Mean Absolute
Deviation is equal to two,

00:08:36.933 --> 00:08:38.439
while for this data set,

00:08:38.439 --> 00:08:41.173
the Mean Absolute
Deviation is equal to one.

00:08:41.173 --> 00:08:42.144
And that makes sense.

00:08:42.144 --> 00:08:43.937
They have the exact same means.

00:08:43.937 --> 00:08:45.445
They both have a mean of three.

00:08:45.445 --> 00:08:47.004
But this one is more spread out.

00:08:47.004 --> 00:08:48.581
The one on the right is more spread out

00:08:48.581 --> 00:08:51.201
because, on average, each of these points

00:08:51.201 --> 00:08:53.309
are two away from three,

00:08:53.309 --> 00:08:55.274
while on average, each of these points

00:08:55.274 --> 00:08:57.707
are one away from three.

00:08:57.707 --> 00:09:01.077
The means of the absolute
deviations on this one is one.

00:09:01.077 --> 00:09:04.245
The means of the absolute
deviations on this one is two.

00:09:04.245 --> 00:09:07.741
So the green one is more
spread out from the mean.


Median and range puzzle

WEBVTT
Kind: captions
Language: en

00:00:00.360 --> 00:00:02.519
- [Voiceover] Let's say that
we run a car dealership,

00:00:02.519 --> 00:00:04.788
and we have 11 salespeople,

00:00:04.788 --> 00:00:07.359
and we record the number of cars

00:00:07.359 --> 00:00:11.139
each of the 11 salespeople
sold in the past week.

00:00:11.139 --> 00:00:15.379
So that's one of them,
two, three, four, five,

00:00:15.379 --> 00:00:18.589
six, seven, eight, nine, 10, 11.

00:00:18.589 --> 00:00:21.379
So we record how much each of them sold.

00:00:21.379 --> 00:00:24.979
So maybe one person sold,
maybe they sold five cars.

00:00:24.979 --> 00:00:27.239
Maybe the next person sold seven cars.

00:00:27.239 --> 00:00:29.499
Maybe the next person sold 10 cars.

00:00:29.499 --> 00:00:31.142
And so that's how we would do it.

00:00:31.142 --> 00:00:33.499
So we're going to record all of that.

00:00:33.499 --> 00:00:37.685
But then we're told that
the median car sold is six.

00:00:37.685 --> 00:00:39.759
So if we ordered all of these numbers,

00:00:39.759 --> 00:00:41.699
so let's just assume
that we ordered them all

00:00:41.699 --> 00:00:43.499
from least to greatest.

00:00:43.499 --> 00:00:45.539
So maybe, and I'm just
making up numbers here,

00:00:45.539 --> 00:00:46.699
maybe this is four.

00:00:46.699 --> 00:00:48.119
This is four.

00:00:48.119 --> 00:00:53.119
Maybe this is five,
five, five, six, seven,

00:00:53.399 --> 00:00:57.439
seven, eight, nine, 10.

00:00:57.439 --> 00:00:59.819
The median car sold, meaning
that the middle number here

00:00:59.819 --> 00:01:01.179
is going to be six.

00:01:01.179 --> 00:01:03.379
Now we don't know whether
all of these other numbers

00:01:03.379 --> 00:01:04.799
are the actual numbers.

00:01:04.799 --> 00:01:05.803
I just made those up.

00:01:05.803 --> 00:01:08.099
But we know that the middle
number needs to be six.

00:01:08.099 --> 00:01:10.419
So let me just fill out
only the middle number.

00:01:10.419 --> 00:01:12.699
So the middle number, if
you have 11 data points,

00:01:12.699 --> 00:01:14.535
the middle number's going
to have five on either side.

00:01:14.535 --> 00:01:15.719
So that's that one right over there.

00:01:15.719 --> 00:01:17.059
One, two, three, four, five.

00:01:17.059 --> 00:01:19.659
One, two, three, four, five.

00:01:19.659 --> 00:01:22.165
So we know that the median,
we know the median--

00:01:22.165 --> 00:01:23.617
Actually, let me do that a purple color.

00:01:23.617 --> 00:01:27.619
The median is going to be six.

00:01:27.619 --> 00:01:28.848
Now the other thing we know is that

00:01:28.848 --> 00:01:32.272
the range of cars sold is four.

00:01:32.272 --> 00:01:33.519
Now let's remind ourselves,

00:01:33.519 --> 00:01:36.499
the range is the maximum
number of cars sold

00:01:36.499 --> 00:01:39.079
minus the minimum number of cars sold,

00:01:39.079 --> 00:01:41.880
and if we have sorted all of these out,

00:01:41.880 --> 00:01:43.519
if we take--

00:01:43.519 --> 00:01:45.548
If this is our max right over here,

00:01:45.548 --> 00:01:47.339
because we've sorted them all out,

00:01:47.339 --> 00:01:50.279
and this is our min right over here,

00:01:50.279 --> 00:01:55.279
our range is going to be
our max minus our min.

00:01:55.360 --> 00:01:56.884
So let me write that down.

00:01:56.884 --> 00:01:58.731
So you take your min and your max.

00:01:58.731 --> 00:02:00.608
You have your range.

00:02:00.608 --> 00:02:05.608
Range is equal to the
maximum minus the minimum.

00:02:05.837 --> 00:02:07.479
And they're telling us that that is four.

00:02:07.479 --> 00:02:09.179
This range is four.

00:02:09.179 --> 00:02:10.659
So the maximum minus the minimum,

00:02:10.659 --> 00:02:14.099
the difference between the number of cars

00:02:14.099 --> 00:02:16.259
that the most productive salesperson sold

00:02:16.259 --> 00:02:17.579
and the number of cars

00:02:17.579 --> 00:02:19.069
that the least productive
salesperson sold,

00:02:19.069 --> 00:02:22.117
that difference is going to be four.

00:02:22.117 --> 00:02:24.129
So given all of those assumptions,

00:02:24.129 --> 00:02:26.259
giving all of that information,

00:02:26.259 --> 00:02:28.981
I'm now going to give you a statement,

00:02:28.981 --> 00:02:32.319
and our challenge is if we assume

00:02:32.319 --> 00:02:34.155
everything I just said is true,

00:02:34.155 --> 00:02:36.651
is this statement going to be true,

00:02:36.651 --> 00:02:38.439
or is this statement going to be false,

00:02:38.439 --> 00:02:40.319
or do we not know?

00:02:40.319 --> 00:02:42.259
So let me write this down.

00:02:42.259 --> 00:02:46.688
So is this going to be true, false,

00:02:48.224 --> 00:02:49.455
or do we not know?

00:02:49.455 --> 00:02:51.619
Do we not have enough information to say

00:02:51.619 --> 00:02:53.739
it's for sure going to be true,

00:02:53.739 --> 00:02:55.619
for sure going to be false,

00:02:55.619 --> 00:02:57.519
or for sure we don't know?

00:02:57.519 --> 00:02:59.499
And so I encourage you
to pause the video now

00:02:59.499 --> 00:03:00.563
and try it out.

00:03:01.163 --> 00:03:03.019
All right, so let's work
through it together.

00:03:03.019 --> 00:03:04.939
This is kind of a fun puzzle here,

00:03:04.939 --> 00:03:06.579
where we've been given some clues,

00:03:06.579 --> 00:03:07.459
and then we have a statement,

00:03:07.459 --> 00:03:09.779
and we figure out can
we make this statement.

00:03:09.779 --> 00:03:12.619
Can we say it's true or can we
say for sure that it's false,

00:03:12.619 --> 00:03:14.600
or do we just not know?

00:03:14.600 --> 00:03:18.445
So a couple of ways to tackle it.

00:03:18.445 --> 00:03:20.580
One way to tackle it is, well look,

00:03:20.580 --> 00:03:23.988
one of the salespeople
must have sold six cars.

00:03:23.988 --> 00:03:25.888
If the median sold is six,

00:03:25.888 --> 00:03:28.539
and there's 11 salespeople here,

00:03:28.539 --> 00:03:31.199
the middle number here,
that if we order it,

00:03:31.199 --> 00:03:34.779
one of them must have sold six cars.

00:03:34.779 --> 00:03:36.179
If we had an even number here,

00:03:36.179 --> 00:03:37.942
then that would be the
average of the two middles,

00:03:37.942 --> 00:03:39.106
but if we have an odd number here,

00:03:39.106 --> 00:03:44.106
that is literally the
middle number of cars sold.

00:03:44.606 --> 00:03:46.845
So someone sold six cars.

00:03:46.845 --> 00:03:48.059
So if we assume--

00:03:49.428 --> 00:03:51.959
We're trying to find a
world where someone sold

00:03:51.959 --> 00:03:54.043
more than 10 cars.

00:03:54.043 --> 00:03:56.538
So if someone sold six cars,

00:03:56.538 --> 00:03:58.799
is there a way, with a range of four,

00:03:58.799 --> 00:04:00.814
that someone sold more than 10?

00:04:01.752 --> 00:04:03.115
Well let's just think about it.

00:04:03.115 --> 00:04:05.051
Let's just assume that the min is six.

00:04:05.051 --> 00:04:06.387
We don't know that the min is six,

00:04:06.387 --> 00:04:08.119
but let's just try it out.

00:04:08.119 --> 00:04:12.316
If the minimum is six,
if the minimum is six,

00:04:12.316 --> 00:04:14.539
what's the maximum going to be?

00:04:14.539 --> 00:04:18.989
Well remember, the range is equal to--

00:04:18.989 --> 00:04:20.549
We know that the range is four.

00:04:20.549 --> 00:04:24.839
The range is equal to the
maximum minus the minimum,

00:04:24.839 --> 00:04:27.479
maximum minus the minimum,

00:04:27.479 --> 00:04:32.479
and so the maximum in this
case would be 10, would be 10.

00:04:33.392 --> 00:04:37.905
The max would be equal
to, would be equal to 10.

00:04:37.905 --> 00:04:40.597
If the min is equal to
six, and instead of colons

00:04:40.597 --> 00:04:41.797
I'm going to write an equals sign,

00:04:41.797 --> 00:04:43.435
if the min is equal to six,

00:04:43.435 --> 00:04:46.705
then the max at most can be equal to 10.

00:04:46.705 --> 00:04:48.112
And we can't take a higher min,

00:04:48.112 --> 00:04:49.719
because we know that the six

00:04:49.719 --> 00:04:51.839
is going to be one of the values.

00:04:51.839 --> 00:04:53.480
We could try a lower minimum value.

00:04:53.480 --> 00:04:55.439
We could say the minimum
value is five or four

00:04:55.439 --> 00:04:56.919
or three or two or one,

00:04:56.919 --> 00:04:58.831
but then the maximum
would go down even more,

00:04:58.831 --> 00:05:00.779
because remember, the
maximum is no more than

00:05:00.779 --> 00:05:02.539
four larger than the minimum.

00:05:02.539 --> 00:05:04.199
So if we assume six, and we know that

00:05:04.199 --> 00:05:06.479
one of the salespeople sold six cars,

00:05:06.479 --> 00:05:08.519
then the maximum that
any of the salespeople

00:05:08.519 --> 00:05:10.879
could have sold is 10.

00:05:10.879 --> 00:05:12.539
And so the statement, at
least one of the salespeople

00:05:12.539 --> 00:05:16.142
sold more than 10 cars,
that's got to be false.

00:05:16.142 --> 00:05:18.399
That's got to be false.

00:05:18.399 --> 00:05:20.399
Now there's another way that
you could think about it.

00:05:20.399 --> 00:05:24.039
You could assume that
someone sold more than 10.

00:05:24.039 --> 00:05:25.700
You could assume.

00:05:25.700 --> 00:05:28.059
In the last example, or the
last way of thinking about it,

00:05:28.059 --> 00:05:31.419
we assumed that the min was six,

00:05:31.419 --> 00:05:33.306
but now let's just assume,

00:05:33.321 --> 00:05:36.011
let's just assume that someone sold--

00:05:36.011 --> 00:05:37.459
Let's just try it out.

00:05:37.459 --> 00:05:38.249
Let's see if it's possible.

00:05:38.249 --> 00:05:41.277
Let's just assume that the max is 11,

00:05:41.277 --> 00:05:43.559
that someone sold more than 10 cars.

00:05:43.559 --> 00:05:46.339
If the max is equal to 11,

00:05:46.339 --> 00:05:48.659
what's the min going to need to be?

00:05:48.659 --> 00:05:50.119
Well we just have to remind ourselves,

00:05:50.119 --> 00:05:52.619
range is equal to max minus min.

00:05:52.619 --> 00:05:56.433
So four is equal to the maximum, 11,

00:05:56.433 --> 00:05:58.234
minus the minimum.

00:05:58.234 --> 00:06:01.619
So 11 minus what is equal to four?

00:06:01.619 --> 00:06:04.319
Well 11 minus seven is equal to four.

00:06:04.319 --> 00:06:06.359
So if we assume that the maximum is 11,

00:06:06.359 --> 00:06:09.659
then the minimum is going to have to be,

00:06:09.659 --> 00:06:13.399
the minimum is going to
have to be equal to seven.

00:06:13.399 --> 00:06:17.495
Now can the minimum be seven
when your median is six?

00:06:17.495 --> 00:06:18.354
No.

00:06:18.354 --> 00:06:20.619
If your median is six,
that means you have--

00:06:20.619 --> 00:06:24.499
That means if you have an
odd number of data points,

00:06:24.499 --> 00:06:26.239
that means one of the data points is six,

00:06:26.239 --> 00:06:27.859
and if you had an even
number of data points,

00:06:27.859 --> 00:06:29.905
that means that the middle two

00:06:29.905 --> 00:06:31.351
are going to average out to be six,

00:06:31.351 --> 00:06:33.119
which means you even have data points

00:06:33.119 --> 00:06:34.399
that are less than six.

00:06:34.399 --> 00:06:36.819
So your minimum can't be seven.

00:06:36.819 --> 00:06:40.059
You're going to have a value
that is at least as low,

00:06:40.059 --> 00:06:41.879
at least as low as six.

00:06:41.879 --> 00:06:45.799
So your assumption can't
be true, can't be true,

00:06:45.799 --> 00:06:48.459
so once again, the assumption
based on the statement

00:06:48.459 --> 00:06:49.499
can't be true.

00:06:49.499 --> 00:06:52.219
This statement is going to be false.


How to find a missing value given the mean

WEBVTT
Kind: captions
Language: en

00:00:00.416 --> 00:00:02.815
- [Voiceover] Let's say you're
in the babysitting business

00:00:02.815 --> 00:00:06.430
and you like to keep a log
of whom you are babysitting.

00:00:06.430 --> 00:00:10.069
So in the last month
you babysat six children

00:00:10.069 --> 00:00:13.666
and you wrote the ages of
all six children in your log.

00:00:13.666 --> 00:00:15.137
But then when you go back
to your log you notice

00:00:15.137 --> 00:00:18.297
that some blue ink spilled
over one of the ages

00:00:18.297 --> 00:00:21.632
and you forgot how old that child is.

00:00:21.632 --> 00:00:22.898
And at first you're really worried,

00:00:22.898 --> 00:00:27.450
your whole system of
keeping records seems to...

00:00:27.450 --> 00:00:29.433
you know, you've lost information.

00:00:29.433 --> 00:00:31.084
But then you remember that every time

00:00:31.084 --> 00:00:34.350
you wrote down a new age that month,

00:00:34.350 --> 00:00:36.334
you recalculated the mean.

00:00:36.334 --> 00:00:38.668
And so you have the
mean here of being four,

00:00:38.668 --> 00:00:41.801
the mean age is four for the six children.

00:00:41.801 --> 00:00:44.802
So given that, given
that you know the mean,

00:00:44.802 --> 00:00:47.301
and that you know five
out of six of the ages,

00:00:47.301 --> 00:00:50.037
can you figure out what the sixth age is?

00:00:50.037 --> 00:00:51.750
And I encourage you to pause the video

00:00:51.750 --> 00:00:54.234
and try to figure it out on your own.

00:00:54.945 --> 00:00:56.628
So assuming you've had a shot at it.

00:00:56.628 --> 00:00:58.612
So let's just call this missing age,

00:00:58.612 --> 00:01:00.547
let's call that question mark.

00:01:00.547 --> 00:01:02.580
So let's just think about
how do we calculate,

00:01:02.580 --> 00:01:03.918
how would we calculate a mean

00:01:03.918 --> 00:01:06.605
if we knew what question mark is?

00:01:06.605 --> 00:01:08.415
Well, we would take the total.

00:01:08.923 --> 00:01:10.892
We would take the total of ages,

00:01:11.643 --> 00:01:13.619
of ages,

00:01:13.619 --> 00:01:15.194
we would then divide that

00:01:15.194 --> 00:01:18.508
by the number of children.

00:01:18.508 --> 00:01:21.583
We then divide that by the number

00:01:21.583 --> 00:01:24.217
of ages that we had,

00:01:24.217 --> 00:01:26.532
and then that would be equal to,

00:01:26.532 --> 00:01:29.281
that would be equal to the mean.

00:01:29.281 --> 00:01:30.416
Or another way to think about it,

00:01:30.416 --> 00:01:33.954
if you multiply both sides
times the number of ages,

00:01:33.954 --> 00:01:37.802
the number of ages on that side

00:01:37.802 --> 00:01:42.329
and the number of ages on that side,

00:01:43.087 --> 00:01:44.921
then this is gonna cancel with that,

00:01:44.921 --> 00:01:46.880
and we're gonna be left with the total

00:01:47.887 --> 00:01:51.615
The total is going to be equal to,

00:01:51.615 --> 00:01:53.528
is going to be equal to the mean

00:01:54.667 --> 00:01:57.073
times the number of ages.

00:01:57.073 --> 00:02:00.103
Mean times, and I'll just
write times the number,

00:02:00.103 --> 00:02:03.006
times number of data points,

00:02:03.006 --> 00:02:05.671
or number of ages.

00:02:05.671 --> 00:02:07.187
So maybe we can use this information,

00:02:07.187 --> 00:02:08.624
'cause we're just going to have this

00:02:08.624 --> 00:02:09.938
missing question mark here and

00:02:09.938 --> 00:02:12.080
we know the mean and we
know the number of ages.

00:02:12.080 --> 00:02:13.937
So we just have to solve
for the question mark.

00:02:13.937 --> 00:02:15.037
So let's do that.

00:02:15.037 --> 00:02:16.338
So let's go back to the beginning here,

00:02:16.338 --> 00:02:18.838
just so this makes
sense with some numbers.

00:02:18.838 --> 00:02:21.696
The total of ages, that's going to be

00:02:21.696 --> 00:02:25.992
five plus two

00:02:25.992 --> 00:02:27.827
plus question mark,

00:02:28.606 --> 00:02:32.990
plus question mark, plus two, this two,

00:02:32.990 --> 00:02:37.241
plus two plus four plus eight.

00:02:37.241 --> 00:02:40.157
We're gonna divide by the number of ages.

00:02:40.157 --> 00:02:42.076
We're gonna divide it
by the number of ages.

00:02:42.076 --> 00:02:43.638
Well we have six ages here.

00:02:43.638 --> 00:02:46.156
One, two, three, four, five, six.

00:02:46.156 --> 00:02:47.340
Six ages.

00:02:47.340 --> 00:02:49.193
And that's going to be equal to the mean.

00:02:49.926 --> 00:02:52.394
This is going to be equal to the mean.

00:02:52.394 --> 00:02:54.845
The mean here is four.

00:02:54.845 --> 00:02:57.375
So let's see, and this is just
how you calculate the mean.

00:02:57.375 --> 00:03:00.126
So let's see if we can simplify this.

00:03:00.126 --> 00:03:03.558
So five plus two is seven.

00:03:04.844 --> 00:03:06.795
Let me do this, that's the wrong color.

00:03:06.795 --> 00:03:10.378
Five plus two, five plus two is seven.

00:03:10.378 --> 00:03:12.948
Two plus four is six plus eight is 14.

00:03:13.682 --> 00:03:14.347
14.

00:03:14.347 --> 00:03:16.734
And then seven plus 14 is 21.

00:03:17.768 --> 00:03:20.252
So we're left with 21 plus question mark

00:03:20.252 --> 00:03:22.351
over six is equal to four.

00:03:22.351 --> 00:03:24.917
Now we can do what we did
when we just wrote it all out.

00:03:24.917 --> 00:03:27.752
We can multiply both sides
times the number of ages,

00:03:27.752 --> 00:03:28.936
the number of data points we have.

00:03:28.936 --> 00:03:31.209
So we can multiply both sides times six.

00:03:32.109 --> 00:03:34.060
We can multiply both sides,

00:03:34.060 --> 00:03:36.658
both sides times six.

00:03:36.658 --> 00:03:39.893
So six on that side, six on this side.

00:03:39.893 --> 00:03:42.942
Six in the numerator, six in
the denominator, those cancel.

00:03:42.942 --> 00:03:44.610
So all we're left is,

00:03:44.610 --> 00:03:49.125
on the left-hand side we're
left with 21 plus question mark.

00:03:49.125 --> 00:03:51.340
Alright. All of these other green numbers,

00:03:51.340 --> 00:03:52.274
those just simplified,

00:03:52.274 --> 00:03:55.208
five plus two plus two
plus four plus eight is 21

00:03:55.208 --> 00:03:56.520
and we still have the question mark.

00:03:56.520 --> 00:03:59.804
So we get 21 plus question mark,

00:03:59.804 --> 00:04:01.147
I want to do that green color,

00:04:02.392 --> 00:04:05.357
21 plus this question mark,

00:04:05.357 --> 00:04:06.871
the thing that we're trying to solve for.

00:04:06.871 --> 00:04:10.460
The missing number is
going to be equal to,

00:04:10.460 --> 00:04:12.272
is going to be equal to

00:04:13.386 --> 00:04:15.353
four times six.

00:04:15.353 --> 00:04:16.885
Well what's four times six?

00:04:16.885 --> 00:04:18.536
That's 24.

00:04:19.203 --> 00:04:20.587
And so what's the question mark?

00:04:20.587 --> 00:04:23.705
21 plus what is equal to 24?

00:04:23.705 --> 00:04:24.721
And we could, of course,

00:04:24.721 --> 00:04:27.105
you might just say, well
it's gonna be three.

00:04:27.105 --> 00:04:28.404
Or, if you want to, you could say well,

00:04:28.404 --> 00:04:30.205
question mark is going to be,

00:04:30.205 --> 00:04:32.915
question mark is going to be equal to,

00:04:33.770 --> 00:04:37.729
is going to be equal to 24 minus 21.

00:04:37.729 --> 00:04:39.307
Which is, of course, three.

00:04:40.116 --> 00:04:42.367
Which of course, so let
me just write this down,

00:04:42.367 --> 00:04:46.116
so the question mark is equal to three.

00:04:46.116 --> 00:04:48.431
So the missing age, you
were able to figure it out

00:04:48.431 --> 00:04:49.900
based on the information you had,

00:04:49.900 --> 00:04:51.165
because you had the mean,

00:04:51.165 --> 00:04:54.067
you were able to figure out
that behind this blotch,

00:04:54.067 --> 00:04:58.240
that behind this blotch you had a three.

00:04:58.994 --> 00:05:00.443
It's exciting.


How to interpret a histogram

WEBVTT
Kind: captions
Language: en

00:00:00.424 --> 00:00:03.153
Let's say you have a cherry pie store.

00:00:03.153 --> 00:00:04.520
and you've noticed that

00:00:04.520 --> 00:00:06.602
there is variability in the number of cherries

00:00:06.602 --> 00:00:09.181
on each pie that you sell.

00:00:09.181 --> 00:00:11.665
Some pies might have over 100 cherries,

00:00:11.665 --> 00:00:15.381
while other pies might have fewer than 50 cherries.

00:00:15.381 --> 00:00:16.560
So what you're curious about is

00:00:16.560 --> 00:00:17.621
what is the distribution,

00:00:17.621 --> 00:00:20.401
how many of different types of pies do you have?

00:00:20.401 --> 00:00:22.289
how may pies do you have that have a lot of cherries,

00:00:22.289 --> 00:00:25.072
how many pies that have a few cherries,

00:00:25.072 --> 00:00:27.461
how many pies are in between?

00:00:27.461 --> 00:00:29.486
So, to do that, you set up a histogram.

00:00:29.486 --> 00:00:32.881
what you do is you take each pie in your store,

00:00:32.881 --> 00:00:36.779
(See I can draw a pie in some kind)

00:00:36.779 --> 00:00:40.991
it's a cherry pie, I don't know if this is adequate of drawing of a pie.

00:00:40.991 --> 00:00:44.133
You take each pie in your store,

00:00:44.133 --> 00:00:49.134
and you count the number of cherries on it.

00:00:49.134 --> 00:00:50.927
This pie has 1,2,3,4,5

00:00:50.927 --> 00:00:54.277
6,7,8,9,10,keep counting

00:00:54.277 --> 00:00:56.701
Let's say it has 32 cherries.

00:00:56.701 --> 00:00:58.148
And you are going to do it for every pie.

00:00:58.148 --> 00:00:59.888
and then you create buckets.

00:00:59.888 --> 00:01:01.921
Because you don't want to create just a graph

00:01:01.921 --> 00:01:03.521
I'm not having exactly 32.

00:01:03.521 --> 00:01:05.187
You just want to get a general sense of things.

00:01:05.187 --> 00:01:08.737
So you create buckets of 30

00:01:08.737 --> 00:01:12.076
you say how many pies have between 0 and 29 cherries?

00:01:12.076 --> 00:01:16.656
how many pies are between 30 and 59, including 30 and 59?

00:01:16.656 --> 00:01:19.987
how many pies have at least 60 at most 89 cherries?

00:01:19.987 --> 00:01:23.303
how many pies have at least 90 at most 119?

00:01:23.303 --> 00:01:27.677
and then how many pies have at least 120 and at most 149?

00:01:27.677 --> 00:01:30.966
you know that you don't have any pie that have more than 149 cherries

00:01:30.966 --> 00:01:32.523
so this should account for everything.

00:01:32.523 --> 00:01:33.503
Then you count them

00:01:33.503 --> 00:01:37.391
so for example, 5 pies have more than 30 to 59 cherries

00:01:37.391 --> 00:01:39.029
and so we create a histogram

00:01:39.029 --> 00:01:43.375
when you create a histogram, you make this magenta bar go up to 5

00:01:43.375 --> 00:01:45.789
so that's how you would construct this histogram

00:01:45.789 --> 00:01:49.736
that's what the pies at different cherry levels histogram is telling us.

00:01:49.736 --> 00:01:52.713
so now we have construct it; Let's see if we can interpret it

00:01:52.713 --> 00:01:56.084
based on the information given in the histogram.

00:01:56.084 --> 00:01:57.560
So the first question is:

00:01:57.560 --> 00:01:59.293
based on just this information

00:01:59.293 --> 00:02:00.704
can you figure out the total

00:02:00.704 --> 00:02:03.112
number of pies in your store?

00:02:03.112 --> 00:02:05.269
soon be there all accounted for by this histogram

00:02:05.269 --> 00:02:06.610
and I encourage you to pause this video

00:02:06.610 --> 00:02:08.680
and try to figure it out on your own

00:02:08.680 --> 00:02:10.938
What was the total number of pies?

00:02:10.938 --> 00:02:13.457
Let's see. There's five pies

00:02:13.457 --> 00:02:21.573
there's five pies that have ... at least 30 cherries but no more than 59.

00:02:21.573 --> 00:02:24.697
you have eight pies in this blue bucket

00:02:24.697 --> 00:02:27.886
you have four pies in this green bucket

00:02:27.886 --> 00:02:31.235
and then you have ... three pies

00:02:31.235 --> 00:02:35.234
that have at least 120 but no more than 149 cherries

00:02:35.234 --> 00:02:37.935
this accounts for all the pies

00:02:37.935 --> 00:02:40.275
so the total number of pies you have at the store

00:02:40.275 --> 00:02:44.689
5 plus 8 plus 4 plus 3

00:02:44.689 --> 00:02:48.568
which is what, 5 plus 8 is 13

00:02:48.568 --> 00:02:51.756
plus 4,=17, plus 3 is twenty.

00:02:51.756 --> 00:02:55.370
So there are 20 pies in this store.

00:02:55.370 --> 00:02:57.239
Then you can ask more a more nuance question.

00:02:57.239 --> 00:03:01.258
what if you want to know the number of pies with more than 60 cherries

00:03:01.258 --> 00:03:03.242
the number of pies with more than 60

00:03:03.242 --> 00:03:08.157
number of pies with

00:03:08.157 --> 00:03:09.922
I'll say this 60 or more

00:03:09.922 --> 00:03:15.861
60 or more cherries

00:03:15.861 --> 00:03:17.427
so let's think about it.

00:03:17.427 --> 00:03:19.721
well this magenta bar doesn't apply

00:03:19.721 --> 00:03:21.436
because these all have less than 60

00:03:21.436 --> 00:03:25.024
but all these other bars are accounting pies that have 60 or more cherries

00:03:25.024 --> 00:03:27.538
this is 60 to 89, this is 90 to 119

00:03:27.538 --> 00:03:30.341
this is a 120 to 149

00:03:30.341 --> 00:03:32.289
so it's going to be these eight cherries

00:03:32.289 --> 00:03:36.653
sorry, these eight pies that are in this bucket

00:03:36.653 --> 00:03:41.182
plus these four pies, plus these three pies

00:03:41.182 --> 00:03:45.309
so it is going to be essentially everything but this first bucket

00:03:45.309 --> 00:03:47.802
everything but all the pies except for these five pies

00:03:47.802 --> 00:03:49.568
have 60 or more cherries

00:03:49.568 --> 00:03:51.506
so should be five less than 20

00:03:51.506 --> 00:03:54.179
Let's see. 8+4=12,plus 3 is 15

00:03:54.179 --> 00:03:56.721
which is five less than 20.

00:03:56.721 --> 00:03:58.005
So using this histogram

00:03:58.005 --> 00:03:59.309
we can answer really interest question, which would say

00:03:59.309 --> 00:04:04.130
how many more pies do we have that have 60-89 cherries

00:04:04.130 --> 00:04:06.848
than 120 to 149 cherries?

00:04:06.848 --> 00:04:09.386
We have eight pies at 60-89

00:04:09.386 --> 00:04:12.285
60-89 cherries, three that have a 120-149

00:04:12.285 --> 00:04:16.581
We have five more pies in the 60 to 89 category

00:04:16.581 --> 00:04:20.528
that we do in the 120 to 149 categories

00:04:20.528 --> 00:04:22.731
A lot of questions that we can start to answer

00:04:22.731 --> 00:04:24.155
hopefully this gives you a sense

00:04:24.155 --> 00:04:27.969
of how you can interpret histograms.


How to create a histogram

WEBVTT
Kind: captions
Language: en

00:00:00.417 --> 00:00:01.972
- [Voiceover] So let's say
you were to go to a restaurant

00:00:01.972 --> 00:00:03.942
and just out of curiosity you want to see

00:00:03.942 --> 00:00:06.978
what the makeup of the
ages at the restaurant are.

00:00:06.978 --> 00:00:08.302
So you go around the restaurant

00:00:08.302 --> 00:00:10.483
and you write down everyone's age.

00:00:10.483 --> 00:00:12.435
And so these are the ages of everyone

00:00:12.435 --> 00:00:14.593
in the restaurant at that moment.

00:00:14.593 --> 00:00:17.566
And so you're interested
in somehow presenting this,

00:00:17.566 --> 00:00:19.935
somehow visualizing the
distribution of the ages,

00:00:19.935 --> 00:00:21.095
because you want just say, well,

00:00:21.095 --> 00:00:22.303
are there more young people?

00:00:22.303 --> 00:00:23.300
Are there more teenagers?

00:00:23.300 --> 00:00:24.393
Are there more middle-aged people?

00:00:24.393 --> 00:00:26.065
Are there more seniors here?

00:00:26.065 --> 00:00:27.526
And so when you just look at these numbers

00:00:27.526 --> 00:00:29.361
it really doesn't give
you a good sense of it.

00:00:29.361 --> 00:00:31.544
It's just a bunch of numbers.

00:00:31.544 --> 00:00:33.620
And so how could you do that?

00:00:33.620 --> 00:00:34.915
Well one way to think about it,

00:00:34.915 --> 00:00:38.003
is to put these ages
into different buckets,

00:00:38.003 --> 00:00:39.838
and then to think about how many people

00:00:39.838 --> 00:00:41.486
are there in each of those buckets?

00:00:41.486 --> 00:00:42.647
Or sometimes someone might say

00:00:42.647 --> 00:00:44.575
how many in each of those bins?

00:00:44.575 --> 00:00:46.083
So let's do that.

00:00:46.083 --> 00:00:48.788
So let's do buckets or categories.

00:00:49.358 --> 00:00:50.970
So, I like,

00:00:51.540 --> 00:00:53.402
sometimes it's called a bin.

00:00:53.402 --> 00:00:56.723
So the bucket, I like to think
of it more of as a bucket,

00:00:56.723 --> 00:00:59.440
the bucket and then the
number in the bucket.

00:00:59.440 --> 00:01:02.406
The number in the bucket.

00:01:02.406 --> 00:01:05.602
Number, I'll just write the number, oops.

00:01:06.534 --> 00:01:08.017
It's the, oops.

00:01:08.623 --> 00:01:10.317
It's the number (laughing),

00:01:10.317 --> 00:01:12.176
it's the number in the bucket.

00:01:12.176 --> 00:01:13.057
Alright.

00:01:13.057 --> 00:01:14.196
So let's just make buckets.

00:01:14.196 --> 00:01:15.565
Let's make them 10 year ranges.

00:01:15.565 --> 00:01:19.629
So let's say the first
one is ages zero to nine.

00:01:19.629 --> 00:01:21.109
So how many people...

00:01:21.109 --> 00:01:22.943
Why don't we just define
all of the buckets here?

00:01:22.943 --> 00:01:25.719
So the next one is ages 10 to 19,

00:01:25.719 --> 00:01:30.697
then 20 to 29, then 30 to 39,

00:01:30.697 --> 00:01:35.420
and 40 to 49, 50 to 59,

00:01:36.343 --> 00:01:37.909
let me make sure you
can read that properly,

00:01:37.909 --> 00:01:40.045
then you have 60 to 69.

00:01:40.045 --> 00:01:41.531
And I think that covers everyone.

00:01:41.531 --> 00:01:44.363
I don't see anyone 70
years old or older here.

00:01:44.363 --> 00:01:45.640
So then how many people fall into

00:01:45.640 --> 00:01:47.916
the zero to nine-year-old bucket?

00:01:47.916 --> 00:01:52.141
Well it's gonna be one, two, three,

00:01:52.141 --> 00:01:57.133
four, five, six people
fall into that bucket.

00:01:57.133 --> 00:01:59.566
How many people fall into the...

00:01:59.566 --> 00:02:02.980
How many people fall into
the 10 to 19-year-old bucket?

00:02:02.980 --> 00:02:04.628
Well, let's see.

00:02:04.628 --> 00:02:06.709
One, two,

00:02:07.988 --> 00:02:09.173
three.

00:02:09.173 --> 00:02:11.008
Three people.

00:02:11.008 --> 00:02:12.215
And I think you see where this is going.

00:02:12.215 --> 00:02:15.001
What about 20 to 29?

00:02:15.001 --> 00:02:18.833
So that's one, two, three,

00:02:18.833 --> 00:02:21.874
four, five people.

00:02:21.874 --> 00:02:23.918
Five people fall into that bucket.

00:02:23.918 --> 00:02:26.959
Alright, what about 30 to 39?

00:02:26.959 --> 00:02:30.187
We have one, and that's it.

00:02:30.187 --> 00:02:35.136
Only one person in that 30 to
39 bin or bucket or category.

00:02:35.823 --> 00:02:38.842
Alright, what about 40 to 49?

00:02:38.842 --> 00:02:41.953
We have one, two people.

00:02:41.953 --> 00:02:44.089
Two people are in that bucket.

00:02:44.089 --> 00:02:47.456
And then 50 to 59.

00:02:47.456 --> 00:02:50.567
Let's see, you have one, two people.

00:02:50.567 --> 00:02:51.938
Two people.

00:02:51.938 --> 00:02:55.861
And then finally, finally, ages 60-69.

00:02:55.861 --> 00:02:57.301
Let me do that in a different color.

00:02:57.301 --> 00:02:58.810
60 to 69.

00:02:58.810 --> 00:03:02.688
There is one person, right over there.

00:03:02.688 --> 00:03:04.173
So this is one way of thinking about

00:03:04.173 --> 00:03:06.032
how the ages are distributed,
but let's actually

00:03:06.032 --> 00:03:10.466
make a visualization of this.

00:03:10.466 --> 00:03:12.114
And the visualization
that we're gonna create,

00:03:12.114 --> 00:03:13.896
this is called a histogram.

00:03:14.757 --> 00:03:16.241
Histogram.

00:03:17.497 --> 00:03:18.867
Histogram.

00:03:18.867 --> 00:03:20.027
We're taking data that can take on

00:03:20.027 --> 00:03:22.164
a whole bunch of different values,

00:03:22.164 --> 00:03:23.627
we're putting them into categories,

00:03:23.627 --> 00:03:24.694
and then we're gonna plot how many

00:03:24.694 --> 00:03:26.599
folks are in each category.

00:03:26.599 --> 00:03:28.224
How big are each of those?

00:03:28.224 --> 00:03:30.198
How big are each of those categories?

00:03:30.198 --> 00:03:32.635
And actually, I wrote histogram.

00:03:32.635 --> 00:03:35.723
I wrote histograph, I should
have written histogram.

00:03:35.723 --> 00:03:38.348
So a histogram. So let's do this.

00:03:38.348 --> 00:03:39.555
Alright.

00:03:39.555 --> 00:03:42.458
So on this axis, let's see,
the largest category has six.

00:03:42.458 --> 00:03:45.314
So this the number, number of folks.

00:03:45.314 --> 00:03:48.302
And it's gonna go one, two, three,

00:03:48.302 --> 00:03:50.971
four, five, six.

00:03:50.971 --> 00:03:55.220
One, two, three, four, five, six.

00:03:55.220 --> 00:03:56.568
This is the number.

00:03:56.568 --> 00:03:59.586
And on this axis I'm
gonna make the buckets.

00:03:59.586 --> 00:04:01.629
The buckets, and let me
scroll up a little bit.

00:04:01.629 --> 00:04:02.720
Now that I have my data here,

00:04:02.720 --> 00:04:05.019
I don't have to look at my data set again.

00:04:05.019 --> 00:04:07.319
So I have one bucket.

00:04:07.319 --> 00:04:09.281
This is going to be the
zero to nine bucket,

00:04:09.989 --> 00:04:11.349
right over here.

00:04:11.349 --> 00:04:12.766
Zero to nine.

00:04:12.766 --> 00:04:15.783
Then I'm going to have the three...

00:04:15.783 --> 00:04:17.595
Actually, let me just plot them,

00:04:17.595 --> 00:04:18.919
since I have my pen that color.

00:04:18.919 --> 00:04:20.814
So in zero to nine there are six people.

00:04:21.722 --> 00:04:25.507
Zero to nine, there are six people.

00:04:25.507 --> 00:04:27.475
So I'll just plot it like that.

00:04:28.405 --> 00:04:31.167
And then we have the 10 to 19.

00:04:31.167 --> 00:04:32.678
There are three people.

00:04:32.678 --> 00:04:37.461
So 10 to 19, there are three people.

00:04:37.461 --> 00:04:40.333
So I'll do a bar, like this.

00:04:41.983 --> 00:04:45.432
Then, 20 to 29, I have five people.

00:04:46.232 --> 00:04:51.035
20 to 29, which is gonna be this one,

00:04:51.035 --> 00:04:53.751
just getting, I'm writing too big.

00:04:53.751 --> 00:04:57.697
So 20 to 29 is gonna be this bar.

00:04:57.697 --> 00:04:59.197
There's five people.

00:04:59.997 --> 00:05:01.480
Five people there.

00:05:02.249 --> 00:05:04.074
So it'll look like this.

00:05:04.896 --> 00:05:06.117
I should have made the bars wide enough

00:05:06.117 --> 00:05:07.278
so I could write below them.

00:05:07.278 --> 00:05:09.848
But I've already, that
train has already left.

00:05:10.548 --> 00:05:12.149
(laughing) Alright, alright.

00:05:12.149 --> 00:05:14.425
Then 30 to 39, I'll try to write smaller.

00:05:14.425 --> 00:05:18.418
30 to 39, that's gonna be
this bar right over here.

00:05:18.418 --> 00:05:20.299
We have one person.

00:05:20.299 --> 00:05:21.825
One person.

00:05:23.358 --> 00:05:25.773
And then we have 40 to 49.

00:05:25.773 --> 00:05:27.305
We have two people.

00:05:27.305 --> 00:05:30.998
40 to 49, two people.

00:05:30.998 --> 00:05:32.919
So, it looks like this.

00:05:33.918 --> 00:05:35.985
40 to 49, two people.

00:05:35.985 --> 00:05:38.447
Almost there. 50 to 59.

00:05:38.447 --> 00:05:39.885
We have two people.

00:05:39.885 --> 00:05:44.290
50 to 59, we also have two people.

00:05:45.152 --> 00:05:47.404
So that's that right over there.

00:05:47.404 --> 00:05:48.658
That's this category.

00:05:48.658 --> 00:05:51.538
And then finally, 60 to
69 we have one person.

00:05:51.538 --> 00:05:55.833
60 to 69, we have one person.

00:05:55.833 --> 00:05:57.564
We have one person.

00:05:57.564 --> 00:05:59.353
And what I have just constructed,

00:05:59.353 --> 00:06:00.955
I took our data.

00:06:00.955 --> 00:06:02.325
I took our data.

00:06:02.325 --> 00:06:04.609
I put it into buckets that
are kind of representative

00:06:04.609 --> 00:06:06.118
of the categories I care about.

00:06:06.118 --> 00:06:08.250
Zero to nine is kind of young kids.

00:06:08.250 --> 00:06:10.293
10 to 19, I guess you
could call them adolescents

00:06:10.293 --> 00:06:12.057
or roughly teenagers, although, obviously

00:06:12.057 --> 00:06:14.287
if you're 10 you're not
quite a teenager yet.

00:06:14.287 --> 00:06:15.911
And then all the different age groups.

00:06:15.911 --> 00:06:18.443
And then when I counted
the number in each bucket

00:06:18.443 --> 00:06:21.684
and I plotted it, now I
can visually get a sense

00:06:21.684 --> 00:06:24.424
of how are the ages
distributed in this restaurant.

00:06:24.424 --> 00:06:26.351
This must be some type of a restraunt

00:06:26.351 --> 00:06:27.698
that gives away toys or something,

00:06:27.698 --> 00:06:28.858
because there's a lot of younger people.

00:06:28.858 --> 00:06:30.275
Maybe it's very family-friendly.

00:06:30.275 --> 00:06:31.808
So every adult that comes in,

00:06:31.808 --> 00:06:34.269
maybe there's a lot of
young adults with kids,

00:06:34.269 --> 00:06:36.125
or maybe grandparents up here,

00:06:36.125 --> 00:06:39.702
and they just bring a lot
of kids to this restaurant.

00:06:39.702 --> 00:06:41.838
So it gives you a view
of what's going on here.

00:06:41.838 --> 00:06:44.786
Just a lot of kids here, a
lot fewer senior citizens.

00:06:44.786 --> 00:06:47.028
So once again, this is just
a way of visualizing things.

00:06:47.028 --> 00:06:50.372
We took a lot of data that
can take multiple data points.

00:06:50.372 --> 00:06:52.020
Instead of plotting each data point,

00:06:52.020 --> 00:06:53.762
like we might do in a dot plot,

00:06:53.762 --> 00:06:55.457
instead of saying how many
one-year-olds are there?

00:06:55.457 --> 00:06:56.500
Well there's only one one-year old.

00:06:56.500 --> 00:06:57.476
How many three-year-olds are there?

00:06:57.476 --> 00:06:58.731
There's only one three-year old.

00:06:58.731 --> 00:07:00.286
That wouldn't give us much information.

00:07:00.286 --> 00:07:01.772
We would just have these single dots

00:07:01.772 --> 00:07:03.211
if we were doing a dot plot.

00:07:03.211 --> 00:07:05.418
But as a histogram, we're
able to put them into buckets.

00:07:05.418 --> 00:07:06.740
Everybody was like,
hey, you know generally

00:07:06.740 --> 00:07:08.799
between the ages zero and
nine we have six people.

00:07:08.799 --> 00:07:11.933
And so you see that plotted
out, just like that.

00:07:11.933 --> 00:07:13.944
And obviously this doesn't apply just to

00:07:13.944 --> 00:07:15.685
ages of people in a restaurant,

00:07:15.685 --> 00:07:17.891
it applies to all sorts
of data that you might

00:07:17.891 --> 00:07:20.234
want to collect and observe.


Statistical questions

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:04.874
- [Voiceover] As we start
exploring the world of statistics,

00:00:04.874 --> 00:00:06.043
it's worth asking ourself,

00:00:06.043 --> 00:00:09.713
what is the word statistics even mean?

00:00:09.713 --> 00:00:12.880
Statistics is really a
broad category of things

00:00:12.880 --> 00:00:14.645
that you might do with data.

00:00:14.645 --> 00:00:18.568
So it generally deals with
data, collecting data.

00:00:18.568 --> 00:00:19.660
So actually let me write these down.

00:00:19.660 --> 00:00:22.085
It's involving collecting data,

00:00:22.085 --> 00:00:23.765
collecting data.

00:00:23.765 --> 00:00:26.725
You could present data
in tables or charts,

00:00:26.725 --> 00:00:28.141
or just as lists of numbers,

00:00:28.141 --> 00:00:30.138
or however you might do it.

00:00:30.138 --> 00:00:32.483
It is analyzing the data,

00:00:32.483 --> 00:00:36.285
analyzing, analyzing,

00:00:36.285 --> 00:00:37.715
presenting and analyzing data.

00:00:37.715 --> 00:00:40.306
So this whole class of just all this stuff

00:00:40.306 --> 00:00:43.595
that you might do with
data to answer a question

00:00:43.595 --> 00:00:45.330
or try to figure out what's going on,

00:00:45.330 --> 00:00:47.073
or just to learn about the world,

00:00:47.073 --> 00:00:50.020
the whole class of things
is called statistics.

00:00:50.020 --> 00:00:53.068
Now an idea that will
come up very frequently

00:00:53.068 --> 00:00:57.117
in statistics is the
notion of variability.

00:00:57.117 --> 00:00:59.950
Variability.

00:00:59.950 --> 00:01:01.899
In everyday language, variability,

00:01:01.899 --> 00:01:04.161
it's how much something is ...

00:01:04.161 --> 00:01:05.624
How much does it vary?

00:01:05.624 --> 00:01:07.197
How much does it change?

00:01:07.197 --> 00:01:09.172
It's the same notion in statistics.

00:01:09.172 --> 00:01:12.299
In statistics, variability
is the degree to which

00:01:12.299 --> 00:01:14.711
data points are different from each other,

00:01:14.711 --> 00:01:16.741
the degree to which they vary.

00:01:16.741 --> 00:01:18.366
Just as an example of that

00:01:18.366 --> 00:01:20.223
to just make it a little
bit more concrete,

00:01:20.223 --> 00:01:22.243
let's say you were to go to five people,

00:01:22.243 --> 00:01:24.101
and you were to ask them,

00:01:24.101 --> 00:01:28.528
how many bricks did you eat yesterday?

00:01:28.528 --> 00:01:30.076
Each of the people say, well I ...

00:01:30.076 --> 00:01:32.274
Person one says, "I
don't eat bricks at all.

00:01:32.274 --> 00:01:33.914
"I don't even know how to do that.

00:01:33.914 --> 00:01:34.983
"I ate zero bricks."

00:01:34.983 --> 00:01:36.198
Then next person says zero,

00:01:36.198 --> 00:01:37.330
the next person says zero,

00:01:37.330 --> 00:01:38.589
fourth person says zero,

00:01:38.589 --> 00:01:40.400
and the fifth person says zero.

00:01:40.400 --> 00:01:42.035
Fair enough, so that was our data point

00:01:42.035 --> 00:01:43.814
on the different data points on ...

00:01:43.814 --> 00:01:45.045
And I'm already doing statistics

00:01:45.045 --> 00:01:46.444
just by going out there and asking them

00:01:46.444 --> 00:01:48.295
how many bricks they ate.

00:01:48.295 --> 00:01:51.758
Then I ask them how many grapes

00:01:51.758 --> 00:01:53.467
did you eat yesterday?

00:01:53.467 --> 00:01:56.514
The first person says "I ate zero grapes."

00:01:56.514 --> 00:01:58.603
But the next person says
"I survive on grapes.

00:01:58.603 --> 00:02:00.808
"I ate 235 grapes."

00:02:00.808 --> 00:02:02.766
The next person says, "Yeah I like grapes.

00:02:02.766 --> 00:02:04.270
"I ate 17 grapes."

00:02:04.270 --> 00:02:07.642
Then the person after that
says that they five grapes.

00:02:07.642 --> 00:02:10.468
Then next person also survives on grapes,

00:02:10.468 --> 00:02:11.460
even to a larger degree.

00:02:11.460 --> 00:02:14.345
They ate 318 grapes.

00:02:14.345 --> 00:02:16.089
So if you look at these two data sets,

00:02:16.089 --> 00:02:18.725
one is the number of bricks
someone ate yesterday,

00:02:18.725 --> 00:02:20.975
the other one is how many
grapes they ate yesterday,

00:02:20.975 --> 00:02:22.943
you immediately see that
there's more variability here.

00:02:22.943 --> 00:02:24.631
All of these data points are zero,

00:02:24.631 --> 00:02:26.798
while these, they change a good bit

00:02:26.798 --> 00:02:28.795
from data point to data point.

00:02:28.795 --> 00:02:31.783
So we have a sense that
there is more variability

00:02:31.783 --> 00:02:33.610
in this data set.

00:02:33.610 --> 00:02:35.304
Now one of the things we will start doing

00:02:35.304 --> 00:02:38.178
a lot in statistics is try to measure

00:02:38.178 --> 00:02:40.233
how much more, how much variability is.

00:02:40.233 --> 00:02:41.467
How can we can quantify that?

00:02:41.467 --> 00:02:42.744
How can we put a number on it?

00:02:42.744 --> 00:02:44.207
How can we measure variability?

00:02:44.207 --> 00:02:47.208
This is a big aspect of statistics,

00:02:47.208 --> 00:02:48.642
but we won't do that in this video.

00:02:48.642 --> 00:02:50.879
There are future videos for doing that.

00:02:50.879 --> 00:02:53.580
But just as we go into
the world of statistics,

00:02:53.580 --> 00:02:57.391
we should think about
when should our brain

00:02:57.391 --> 00:02:59.275
even start getting into statistics mode,

00:02:59.275 --> 00:03:02.060
thinking about the tools
that we have at our disposal,

00:03:02.060 --> 00:03:05.412
about collecting data and
measuring variability,

00:03:05.412 --> 00:03:07.331
and measuring and finding numbers

00:03:07.331 --> 00:03:11.909
that somehow represent a pool
of data that has variability.

00:03:11.909 --> 00:03:14.160
So the question we should ask ourselves is

00:03:14.160 --> 00:03:17.550
what questions in the world
are statistical questions?

00:03:17.550 --> 00:03:19.202
So statistical,

00:03:20.741 --> 00:03:23.085
statistical questions.

00:03:24.255 --> 00:03:25.092
So let's come up with a

00:03:25.092 --> 00:03:26.925
definition for statistical questions,

00:03:26.925 --> 00:03:28.897
the type of question
where we would want to

00:03:28.897 --> 00:03:33.267
start bringing out our
statistical toolkit.

00:03:33.281 --> 00:03:34.733
One possible way to think about

00:03:34.733 --> 00:03:36.679
when you need to bring out
your statistical toolkit

00:03:36.679 --> 00:03:39.755
is these are questions
that to answer them,

00:03:39.755 --> 00:03:41.323
to answer,

00:03:42.385 --> 00:03:46.153
you need to collect data with variability.

00:03:46.153 --> 00:03:48.584
To answer, you need

00:03:48.584 --> 00:03:50.207
to collect

00:03:51.519 --> 00:03:55.512
data with variability.

00:03:55.512 --> 00:03:57.440
I apologize for my handwriting.

00:03:58.378 --> 00:04:00.458
Data with variability.

00:04:00.458 --> 00:04:02.100
That's W-I-T-H.

00:04:02.100 --> 00:04:03.131
Data with

00:04:06.176 --> 00:04:08.354
variability.

00:04:08.354 --> 00:04:10.930
So you're saying, okay
that kinda makes sense,

00:04:10.930 --> 00:04:12.762
but I need to see some tangible questions

00:04:12.762 --> 00:04:14.552
or tangible examples of things

00:04:14.552 --> 00:04:16.177
that are statistical questions

00:04:16.177 --> 00:04:18.524
and things that are not
statistical questions.

00:04:18.524 --> 00:04:20.032
I would say fair enough.

00:04:20.032 --> 00:04:21.776
Let's look at some examples.

00:04:23.038 --> 00:04:25.636
So here I have six questions,

00:04:25.636 --> 00:04:28.050
and I encourage you to
pause this video right now.

00:04:28.050 --> 00:04:30.019
Before I work through it, think about it.

00:04:30.019 --> 00:04:32.482
Based on this definition
of a statistical question,

00:04:32.482 --> 00:04:34.757
which of these questions are statistical,

00:04:34.757 --> 00:04:37.591
would require your statistical toolkit,

00:04:37.591 --> 00:04:39.878
and which of these are not statistical?

00:04:41.155 --> 00:04:42.517
So assuming you had a go at it,

00:04:42.517 --> 00:04:44.490
let's go through these one by one.

00:04:44.490 --> 00:04:45.514
So the first question,

00:04:45.514 --> 00:04:48.174
how much does my pet grapefruit weigh?

00:04:48.174 --> 00:04:49.367
You know, it's bizarre to begin with

00:04:49.367 --> 00:04:50.968
to have a pet grapefruit,

00:04:50.968 --> 00:04:53.877
but is this a statistical question?

00:04:54.847 --> 00:04:56.053
What do I need to do to answer it?

00:04:56.053 --> 00:04:57.779
I have to take my pet grapefruit out.

00:04:57.779 --> 00:04:59.179
I have to weigh it.

00:04:59.179 --> 00:05:00.673
Then I have to just write that down.

00:05:00.673 --> 00:05:03.094
Just doing that I am collecting data,

00:05:03.094 --> 00:05:06.234
so you could argue that
maybe I'm kinda starting

00:05:06.234 --> 00:05:07.944
to mess with statistics a little bit,

00:05:07.944 --> 00:05:09.988
but I'm just getting one data point.

00:05:09.988 --> 00:05:11.451
So I might weigh it and I might see

00:05:11.451 --> 00:05:14.879
my grapefruit weighs one pound,

00:05:14.879 --> 00:05:17.333
but that's not data with variability.

00:05:17.333 --> 00:05:18.564
That's just one data point.

00:05:18.564 --> 00:05:19.845
In order to have
variability you have to have

00:05:19.845 --> 00:05:21.241
multiple data points

00:05:21.241 --> 00:05:24.607
and should be at least
possible that they could vary.

00:05:24.607 --> 00:05:27.502
So, for example, all of
these folks ate zero bricks

00:05:27.502 --> 00:05:30.961
but maybe it was possible that
someone actually ate a brick.

00:05:30.961 --> 00:05:32.874
But here I have just one data point.

00:05:32.874 --> 00:05:34.848
With one data point, you
can't have variability,

00:05:34.848 --> 00:05:37.216
so this is not a statistical question.

00:05:37.216 --> 00:05:38.841
I just collect a data point.

00:05:38.841 --> 00:05:41.339
Next question, what is the average number

00:05:41.339 --> 00:05:44.165
of cars in a parking
lot on Monday mornings?

00:05:44.165 --> 00:05:46.269
To think about whether it
is a statistical question,

00:05:46.269 --> 00:05:47.153
we just have to think about

00:05:47.153 --> 00:05:49.318
what do I have to do to
answer that question?

00:05:49.318 --> 00:05:51.060
I would have to go out to the parking lot

00:05:51.060 --> 00:05:53.345
on multiple Monday mornings,

00:05:53.345 --> 00:05:55.466
and measure the number of cars.

00:05:55.466 --> 00:05:56.761
So on the first Monday morning

00:05:56.761 --> 00:05:58.409
I might see there are 50 cars.

00:05:58.409 --> 00:06:00.635
The next Monday morning
I might go out there

00:06:00.635 --> 00:06:02.226
and count there's 49 cars.

00:06:02.226 --> 00:06:04.997
The next Monday morning I
might see 50 cars again.

00:06:04.997 --> 00:06:08.575
The next Monday morning
I might see 63 cars.

00:06:08.575 --> 00:06:10.446
So I'm collecting multiple data points

00:06:10.446 --> 00:06:11.586
to answer this question.

00:06:11.586 --> 00:06:13.304
Then I'm going to take
the average of all these,

00:06:13.304 --> 00:06:15.315
but I'm collecting multiple data points

00:06:15.315 --> 00:06:17.452
to answer this question.

00:06:19.128 --> 00:06:21.910
It's definitely possible that
there could be variation here,

00:06:21.910 --> 00:06:23.382
that there could be variability,

00:06:23.382 --> 00:06:26.590
so this is a statistical question.

00:06:26.590 --> 00:06:29.026
Next question, am I hungry?

00:06:29.026 --> 00:06:30.264
It's an important question.

00:06:30.264 --> 00:06:32.539
We ask it to ourselves multiple times.

00:06:32.539 --> 00:06:36.014
In fact, sometimes our
bodies just tell it to us.

00:06:36.014 --> 00:06:37.641
But I am definitely not collecting ...

00:06:37.641 --> 00:06:38.849
I guess you could say I'm collecting

00:06:38.849 --> 00:06:41.215
some type of feelings from my stomach

00:06:41.215 --> 00:06:43.437
or how weak I feel or not,

00:06:43.437 --> 00:06:45.715
but it's definitely not
data with variability.

00:06:45.715 --> 00:06:48.733
I'm either hungry or not
hungry on a given day.

00:06:48.733 --> 00:06:50.311
I mean if you said broader,

00:06:50.311 --> 00:06:52.290
how does my hunger change from day to day

00:06:52.290 --> 00:06:55.448
and you came up some type of a
scale for rating your hunger,

00:06:55.448 --> 00:06:57.314
all right maybe that's more statistical.

00:06:57.314 --> 00:07:00.028
But just am I hungry, a yes-no question.

00:07:00.028 --> 00:07:01.181
This is not ...

00:07:02.104 --> 00:07:03.615
To answer this I do not have to

00:07:03.615 --> 00:07:05.481
collect data with variability,

00:07:05.481 --> 00:07:08.121
so this is not a statistical question.

00:07:08.121 --> 00:07:10.466
How many teeth does my mother have?

00:07:10.466 --> 00:07:12.431
To do this I would have
to go find my mother,

00:07:12.431 --> 00:07:15.344
and then I would have to
ask her to open her mouth,

00:07:15.344 --> 00:07:16.916
and count the teeth in her mouth.

00:07:16.916 --> 00:07:18.797
Maybe I'd get a number like 30.

00:07:18.797 --> 00:07:21.436
So it's kind of like how much
does my pet grapefruit weigh.

00:07:21.436 --> 00:07:25.393
I do have to collect one data point,

00:07:25.393 --> 00:07:28.431
but one data point is not
going to have variability,

00:07:28.431 --> 00:07:30.879
so I am not collecting
data with variability,

00:07:30.879 --> 00:07:32.978
so this is not a statistical question.

00:07:32.978 --> 00:07:35.441
If I said how many teeth
do all of the mothers

00:07:35.441 --> 00:07:37.132
that I know have on average,

00:07:37.132 --> 00:07:39.275
or what's the range of number of teeth

00:07:39.275 --> 00:07:40.432
of the mothers I know have,

00:07:40.432 --> 00:07:43.055
that would be statistical.

00:07:43.055 --> 00:07:45.941
But this is just one data
point, so not statistical.

00:07:45.941 --> 00:07:48.703
How much time do the members of my family

00:07:48.703 --> 00:07:50.834
spend eating per year?

00:07:52.004 --> 00:07:55.987
Once again, what do I need to
do to answer this question?

00:07:55.987 --> 00:07:58.399
I would have to go either observe

00:07:58.399 --> 00:08:00.256
or survey my family members,

00:08:00.256 --> 00:08:03.289
maybe my mom, my wife, my children,

00:08:03.289 --> 00:08:05.523
and my uncles, aunts, whoever else,

00:08:05.523 --> 00:08:07.540
and I would say how much
do you eat each day?

00:08:07.540 --> 00:08:08.863
I would add them all up to figure out

00:08:08.863 --> 00:08:10.216
how much they eat in a year.

00:08:10.216 --> 00:08:12.299
Maybe family member A

00:08:12.299 --> 00:08:15.552
eats 813 hours in a year.

00:08:15.552 --> 00:08:18.561
Family member B ate, I don't know,

00:08:18.561 --> 00:08:22.938
732 hours in the year.

00:08:22.938 --> 00:08:25.718
So you see the general notion
that I will be collecting

00:08:25.718 --> 00:08:28.823
multiple data points from
the different family members.

00:08:28.823 --> 00:08:30.115
There very well, and in fact,

00:08:30.115 --> 00:08:32.947
there's very likely to
be variation in that.

00:08:32.947 --> 00:08:35.009
In fact, I might even see
variation from year to year.

00:08:35.009 --> 00:08:36.170
Person A is probably going to eat

00:08:36.170 --> 00:08:38.581
a different number of
hours in the next year.

00:08:38.581 --> 00:08:41.230
So I'm definitely going to
collect data with variability

00:08:41.230 --> 00:08:43.321
in order to answer this question.

00:08:43.321 --> 00:08:45.527
So that is a statistical question.

00:08:45.527 --> 00:08:47.297
Then finally, I have the question,

00:08:47.297 --> 00:08:50.570
how many times have I watched Star Wars?

00:08:50.570 --> 00:08:53.591
This is very similar to how
many teeth does my mother have,

00:08:53.591 --> 00:08:55.395
or how much does my pet grapefruit weigh.

00:08:55.395 --> 00:08:57.413
I just have to count the number of times

00:08:57.413 --> 00:08:58.599
that I watched Star Wars.

00:08:58.599 --> 00:09:01.061
Maybe I watched it seven times.

00:09:01.061 --> 00:09:02.330
Just one data point.

00:09:02.330 --> 00:09:03.755
No variability here.

00:09:03.755 --> 00:09:06.268
If I said on average how many times

00:09:06.268 --> 00:09:07.879
have my co-workers watched Star Wars,

00:09:07.879 --> 00:09:09.967
then I'm gonna have to
collect data with variability.

00:09:09.967 --> 00:09:11.184
I'm gonna collect multiple data points,

00:09:11.184 --> 00:09:13.610
and it's definitely
possible that my co-workers

00:09:13.610 --> 00:09:15.463
have watched it different
numbers of times.

00:09:15.463 --> 00:09:17.082
But for this question in particular,

00:09:17.082 --> 00:09:18.967
where it's just one
data point to answer it,

00:09:18.967 --> 00:09:20.958
how many times have I watched Star Wars?

00:09:20.958 --> 00:09:23.496
My answer in this case
actually I think is seven.

00:09:23.496 --> 00:09:25.175
Then not a statistical question.

00:09:26.083 --> 00:09:27.760
So hopefully that gives you a sense

00:09:27.760 --> 00:09:29.501
of statistics variability

00:09:29.501 --> 00:09:33.045
and what a statistical question even is.