FINDING A PERCENTILE FOR GROUPED DATA

FINDING A PERCENTILE FOR GROUPED DATA - d(n 1 = 0.25(101 =...

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FINDING A PERCENTILE FOR GROUPED DATA The formula for finding the percentile for grouped data is as follows P d = X k + ( d(n+1) – k ) ( X h - X k ) ( 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) X k is the upper limit of the interval containing k h is the next higher cumulative frequency X h 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 25 th percentile (or the first quartile) d = 0.25
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Unformatted text preview: d (n+1) = 0.25(101) = 25.25 k is the greatest cumulative frequency less than or equal to 25.25, which is 22 X k is the upper limit of the class containing 22, which is 18 h is the next higher cumulative frequency, which is 46 X h is the upper limit of the class containing 46, which is 20 Therefore, substituting the values we have P 0.25 = 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. 70 th or 65 th etc....
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