Question

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 58th, and 68th percentiles. If needed, round your answers to two decimal digits.

Percentile   Value
20%   *

25%   *

58%   *

68% *

Answer 1

solution,

20th percentile = 20

Arrange the data in ascending order: 15, 20, 25, 25, 27, 28, 30, 34

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 20

Answer : the 20th percentile is 20

25th percentile = 22.5

Arrange the data in ascending order: 15, 20, 25, 25, 27, 28, 30, 34

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 (20 and 25 respectively)

Answer : the 25th percentile is (20 + 25) / 2 = 22.5

58th percentile = 27

Arrange the data in ascending order: 15, 20, 25, 25, 27, 28, 30, 34

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

i = (p / 100) * n), where p = 58 and n = 8

i = (58 / 100) * 8 = 4.64

The index i is not an integer, round up. (i = 5) ⇒ the 58th percentile is the value in 5th position, or 27

Answer : the 58th percentile is 27

68th percentile = 28

Arrange the data in ascending order: 15, 20, 25, 25, 27, 28, 30, 34

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

i = (p / 100) * n), where p = 68 and n = 8

i = (68 / 100) * 8 = 5.44

The index i is not an integer, round up. (i = 6) ⇒ the 68th percentile is the value in 6th position, or 28

Answer : the 68th percentile is 28