Question

Consider a sample with data values of 27, 24, 23, 19, 32, 36, 29, and 24. Compute the 20th, 25th, 65th, and 75th percentiles

eBook Consider a sample with data values of 27, 24, 23, 19, 32, 36, 29, and 24. Compute the 20th, 25th, 65th, and 75th percentiles (to 1 decimal, if decimals are necessary). 20th percentile 25th percentile 65th percentile 75th percentile

Answer 1

Arrange the data sets in ascending order (from smallest to largest)

19, 23, 24, 24, 27, 29, 32, 36.

The xth percentile is the [(x/100) * n]th value (rounded up to the nearest integer or average of this value and next value in case of an integer) in the sorted data from smallest to largest.

Where, n is the number of values in the data set.

So, n= 8

20th percentile = (x/100) * n = (20/100) * 8 = 1.6 = 2 (rounded up to the nearest integer)

hence, 20th percentile is 2th value in the sorted data.

20th percentile is 23.

25th percentile = (x/100) * n = (25/100) * 8 = 2 (take a average of 2nd and 3rd value)

25th percentile = (23 + 24)/2 = 23.5

25th percentile is 23.5

65th percentile = (x/100) * n = (65/100) * 8 = 5.2 = 6

Hence, 65th percentile is the 6th value in the sorted data.

65th percentile is 29.

75th percentile = (x/100) * n = (75/100) * 8 = 6 (take a average of 6th and 7th value)

75th percentile = (29+32) / 2 = 30.5

75th percentile is 30.5