A chest physician observed that the distribution of forced expiratory volume (FEV) in 300 smokers had a median value of 2.5 litres with the first and third quailes being 1.5 and 4.5 litres respectively. Based on this data now many persons in the sample are expected to have a FEV between 1.5 and 4.5 litres?
Ans. is 'b' i.e., 150 Quaile The quailes are the four ranges defined by the three value discussed. o A quaile is any of the three values which divide the soed data set into four equal pas, so that each pa represents one fouh of the sample. From above mentioned lines it is very difficult to understand that what the quaile is. I am trying to explain in very simple language : ? o A quaile divides the data into four equal pas. o That means the data will have four equal pas i.e., 25 percent each. o So, the number of intercepts required will be 3, i.e., Q1, Q2, Q3. Q 1 is first (lowest) quale Q2 is second quaile Q3 is third (highest quaile) From above figure it is clear that : - i) Zero - Q I will cover 25% value ii) Zero - Q2 will cover 50 % value iii) Zero - Q3 will cover 75% value . iv) Zero - 100 will cover 100% value Zero - Ql, Ql- Q2, Q2-Q3 and Q3-100 all will cover 25% values among each of them. Zero-Q2, QI-Q3, Q2-100 will cover 50% values. Coming to question The first quaile Q1 = 1.5 litres. The third quaile Q3 = 4.5 litres The value between Q1 - Q3 = 50% (see above) So, 50% of total smokers (300) will have FEV between 1.5 to 4.5 litres. 50% of 300 = 150
75
150
225
300