Question

Consider a sample with data values of 26, 25, 22, 17, 30, 36, 28, and 25. 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

Solution:

20th percentile = 22

Arrange the data in ascending order: 17, 22, 25, 25, 26, 28, 30, 36

Compute the position of the pth percentile (index i):

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 20th percentile is the value in 2th position, or 22

Answer: the 20th percentile is 22

25th percentile = 23.5

Compute the position of the pth percentile (index i):

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

i = (25 / 100) * 8 = 2

The index i is an integer ⇒ the 25th percentile is the average of the values in the 1th and 2th positions (22 and 25 respectively)

Answer: the 25th percentile is (22 + 25) / 2 = 23.5

65th percentile = 28

Compute the position of the pth percentile (index i):

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 65th percentile is the value in 6th position, or 28

Answer: the 65th percentile is 28

75th percentile = 29

Compute the position of the pth percentile (index i):

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

i = (75 / 100) * 8 = 6

The index i is an integer ⇒ the 75th percentile is the average of the values in the 5th and 6th positions (28 and 30 respectively)

Answer: the 75th percentile is (28 + 30) / 2 = 29