Percentiles for Grouped Data:
Percentiles can also be calculated for grouped data which is done with the help of following formulae;
ℓ= 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.
We will calculate thirty-seventh, forty-fifth and ninetieth percentile from the frequency distribution of weights of 120 students, by using the this table.
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.
Find the percentiles P8, P50, and P85 of the following data.
1) find each cumulative frequency and each real interval.
2) Remember the percentile common formula of continuous or discrete distribution (Grouped Data).
ℓ= 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.
ℓ= 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.