A<unk>  is the value of a variable below which a certain percent of observations fall.  So the 20th<unk>  is the value (or score) below which 20 percent of the observations may be found.  The term<unk>  and the related term<unk>  rank are often used in descriptive statistics as well as in the reporting of scores from norm-referenced tests.
The 25th<unk>  is also known as the first quartile; the 50th<unk>  as the median.
There is no standard definition of<unk>  


, however all definitions yield similar results when the number of observations is large. One definition is that the 
p
{\displaystyle p}
-th<unk>  of 
N
{\displaystyle N}
 ordered values is obtained by first calculating the rank 
n
=
N
100
p
+
1
2
{\displaystyle n={\frac {N}{100}}\,p+{\frac {1}{2}}}
, rounding to the nearest integer, and taking the value that corresponds to that rank.
An alternative method, used in many applications, is to use linear interpolation between the two nearest ranks instead of rounding. Specifically, if we have 
N
{\displaystyle N}
 values 
v
1
{\displaystyle v_{1}}
, 
v
2
{\displaystyle v_{2}}
, 
v
3
{\displaystyle v_{3}}
,...,
v
N
{\displaystyle v_{N}}
 , ranked from least to greatest, define the<unk>  corresponding to the 
n
{\displaystyle n}
-th value as 
p
n
=
100
N
(
n
−
1
2
)
.
{\displaystyle p_{n}={\frac {100}{N}}(n-{\frac {1}{2}}).}
 In this way, for example, if 
N
=
5
{\displaystyle N=5}
 the<unk>  corresponding to the third value is 
p
3
=
100
5
(
3
−
1
2
)
=
50.
{\displaystyle p_{3}={\frac {100}{5}}(3-{\frac {1}{2}})=50.}
Suppose we now want to calculate the value 
v
{\displaystyle v}
 corresponding to a<unk>  
p
{\displaystyle p}
. If 
p
<
p
1
{\displaystyle p<p_{1}}
 or 
p
>
p
N
{\displaystyle p>p_{N}}
, we take 
v
=
v
1
{\displaystyle v=v_{1}}
 or 
v
=
v
N
{\displaystyle v=v_{N}}
 respectively. Otherwise, we find an integer 
k
{\displaystyle k}
 such that 
p
k
≤
p
≤
p
k
+
1
{\displaystyle p_{k}\leq p\leq p_{k+1}}
 , and take 
v
=
v
k
+
N
100
(
p
−
p
k
)
(
v
k
+
1
−
v
k
)
.
{\displaystyle v=v_{k}+{\frac {N}{100}}(p-p_{k})(v_{k+1}-v_{k}).}

When 
p
=
50
{\displaystyle p=50}
, the formula gives the median. When 
N
{\displaystyle N}
 is even and 
p
=
25
{\displaystyle p=25}
, the formula gives the median of the first 
N
2
{\displaystyle {\frac {N}{2}}}
 values.
Linked with the<unk>  function, there is also a weighted<unk> , where the percentage in the total weight is counted instead of the total number. In most spreadsheet applications there is no standard function for a weighted<unk> . One method for weighted<unk>  extends the method described above.  Suppose we have positive weights 
w
1
{\displaystyle w_{1}}
, 
w
2
{\displaystyle w_{2}}
, 
w
3
{\displaystyle w_{3}}
,...,
w
N
{\displaystyle w_{N}}
 , associated respectively with our 
N
{\displaystyle N}
 sample values.  Let 
S
n
=
∑
k
=
1
n
w
k
{\displaystyle S_{n}=\sum _{k=1}^{n}w_{k}}
 be the 
n
{\displaystyle n}
-th partial sum of these weights.  Then the formulas above are generalized by taking 
p
n
=
100
S
N
(
S
n
−
w
n
2
)
{\displaystyle p_{n}={\frac {100}{S_{N}}}(S_{n}-{\frac {w_{n}}{2}})}
 and 
v
=
v
k
+
p
−
p
k
p
k
+
1
−
p
k
(
v
k
+
1
−
v
k
)
.
{\displaystyle v=v_{k}+{\frac {p-p_{k}}{p_{k+1}-p_{k}}}(v_{k+1}-v_{k}).}
Percentile
Median
Average
Arithmetic mean
Absolute deviation
Theoretical plate
Dose Profile
Point prevalence