Question

Consider a sample with data values of 26, 25, 20, 15, 31, 33, 29, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.

20th percentile

25th percentile

65th percentile

75th percentile

Answer 1

Ans:

Sorted data:

15,20,25,25,26,29,31,33

20th percentile=20

25th percentile=22.5

65th percentile=29

75th percentile=30

Explanation:

1)

i = (p / 100) * n), where p = 20 and n = 8

i = (20 / 100) * 8 = 1.6

The index i is not an integer, round up. (i = 2) ⇒ the 20^th percentile is the value in 2^th position, or 20

The 20^th percentile is 20

2)

i = (p / 100) * n), where p = 25 and n = 8

i = (25 / 100) * 8 = 2

The index i is an integer ⇒ the 25^th percentile is the average of the values in the 1^th and 2^th positions (20 and 25 respectively)

The 25^th percentile is (20 + 25) / 2 = 22.5

3)

i = (p / 100) * n), where p = 65 and n = 8

i = (65 / 100) * 8 = 5.2

The index i is not an integer, round up. (i = 6) ⇒ the 65^th percentile is the value in 6^th position, or 29

The 65^th percentile is 29

4)

i = (p / 100) * n), where p = 75 and n = 8

i = (75 / 100) * 8 = 6

The index i is an integer ⇒ the 75^th percentile is the average of the values in the 5^th and 6^th positions (29 and 31 respectively)

The 75^th percentile is (29 + 31) / 2 = 30