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Notes - Finding a Percentile for Grouped Data
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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.