From the Following Data, Compute the Value of P₂₇

Given Data

xi	0	1	2	3	4	5	6	7	8
fi	1	9	26	59	72	52	29	7	1

Solution

Percentile divides the dataset into 100 equal parts. To compute P₂₇, we use the following formula:

Formula: P₂₇ = ^27N/₁₀₀

Given N = 256 (total frequency), we have:

P₂₇ = ^{27 x 256}/₁₀₀ = 69.12

Looking at the cumulative frequency (C.F.) table:

xi	fi	C.F.
0	1	1
1	9	10
2	26	36
3	59	95
4	72	167
5	52	219
6	29	248
7	7	255
8	1	256

The cumulative frequency just greater than 69.12 is 95, which corresponds to x_i = 3.

Thus, P₂₇ = 3.

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