FINDING A PERCENTILE FOR GROUPED DATA

FINDING A PERCENTILE FOR GROUPED DATA

The formula for finding the percentile for grouped data is as follows

Pd = Xk + (d(n+1) k ) (Xh - Xk )

( h k )

where

d is the level of the percentile you want to find

k is the greatest cumulative frequency less than or equal to d(n+1)

Xk is the upper limit of the interval containing k

h is the next higher cumulative frequency

Xh is the upper limit of class containing h

EXAMPLE

Class Interval

frequency

cumulative frequency

14 under 16

9

9

16 18

13

22

18 20

24

46

20 22

38

84

22 24

16

100

100

We want to find the 25th percentile (or the first quartile)

d = 0.25

d (n+1) = 0.25(101) = 25.25

k is the greatest cumulative frequency less than or equal to 25.25, which is 22

Xk is the upper limit of the class containing 22, which is 18

h is the next higher cumulative frequency, which is 46

Xh is the upper limit of the class containing 46, which is 20

Therefore, substituting the values we have

P0.25 = 18 + (25.25 22)(20 18) = 18.27

(46 22)

If we want to find the median, then we put d = 0.50 and proceed as above.

It is the same for any other percentile, e.g. 70th or 65th etc.