Question

Find the 94th percentile, P₉₄,  from the following data

11.7	12.3	14.1	14.7	16
17.2	17.4	22	23.1	24.8
25.9	26	26.5	27.1	27.5
28	28.2	28.4	30	31.4
33.1	33.6	35.5	35.7	37.2
37.3	37.8	42	42.3	42.7
44.1	45.3	45.4	47.9	48.3
49.9

Please show work, I have tried to multiply total number of data points (36) by .94 percent to get the answer of 33.84, which I believe should be rounded to 34, leaving the logical answer to be 47.9 however this is NOT the correct answer.

Answer 1

Arranging the data in ascending order we get

11.7, 12.3, 14.1, 14.7, 16, 17.2, 17.4, 22, 23.1, 24.8, 25.9, 26, 26.5, 27.1, 27.5, 28, 28.2, 28.4, 30, 31.4, 33.1, 33.6, 35.5, 35.7, 37.2, 37.3, 37.8, 42, 42.3, 42.7, 44.1, 45.3, 45.4, 47.9, 48.3, 49.9

Percentile is calculated as

i = (p / 100) * n), where p = 94 and n = 36

i = (94 / 100) * 36 = 33.84

Rounding i as 34 hence 47.9 is the correct answer .

or if the distribution is normal we have to use Z score for percentile calculation.

The mean of the data is calculated as

and sample standard as

s=11.042

And Z score at 0.94 using Z table shown below as

Z=1.56 now by Z formula

Hence 47.9 is the closest value which can be correct.