Calculation of Percentiles for Grouped Data

Percentiles for Grouped Data:
Percentiles can also be calculated for grouped data which is done with the help of following formulae;

percentile form 5

Where,
= lower boundary of the class containing the P35 or P99, i.e. the class corresponding to the cumulative frequency in which 35N/100 or 99N/100 lies
w= class interval size of the class containing P35 or P99.
f= frequency of the class containing P35 or P99.
N= number of values, or the total frequency.
C= cumulative frequency of the class preceding the class containing P35 or P99.

For Example:
We will calculate thirty-seventh, forty-fifth and ninetieth percentile from the frequency distribution of weights of 120 students, by using the this table.


=182.83 pounds

Conclusion
From P37, P45 and P90 we have concluded or interpreted that 37% student weigh 147.5 pounds or less. Similarly, 45% students weigh 151.1 pounds or less and 90% students weigh 182.83 pounds or less.

Big Example:
Find the percentiles P8, P50, and P85 of the following data.

Columns Load Frequency
50-69 3
70-89 7
90-109 4
110-129 4
130-149 9

Solution:
1) find each cumulative frequency and each real interval.


2) Remember the percentile common formula of continuous or discrete distribution (Grouped Data).
percentile form 6

= the lower boundary of relevant percentile class
C= the cumulative frequency of the previous interval of relevant percentile class
f= the frequency of relevant percentile class
w= the length of the real interval
4) find eighth percentile.

5) find fiftieth percentile.

6) find eighty-fifth percentile.

7) Find the percentile number of the estimated datum of 115 in the above data.
percentile form 7

= the lower boundary of related percentile class=109.5
C= the cumulative frequency of the previous interval of related percentile class=14
f= the frequency of related percentile class=4
w= the length of the real interval =20

then X=15.1, then the percentile number

Let’s read post Calculation of Quartiles, Deciles & Percentiles for Grouped Data.

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