Question

HELP PLEASE!

find the values of the 30th and 90th percentiles of the data.
129, 113, 200, 100, 105, 132, 100, 176, 146, 152
a. 30th percentile = 105;
90th percentile = 200
b. 30th percentile = 113;
90th percentile = 200
c. 30th = 105;
90th = 176
d. 30th = 113;
90th = 176

Answer 1

30th percentile = 109

Solution:

Step 1. Arrange the data in ascending order: 100, 100, 105, 113, 129, 132, 146, 152, 176, 200

Step 2. Compute the position of the pth percentile (index i):

i = (p / 100) * n), where p = 30 and n = 10

i = (30 / 100) * 10 = 3

Step 3. The index i is an integer ⇒ the 30th percentile is the average of the values in the 2th and 3th positions (105 and 113 respectively)

Answer: the 30th percentile is (105 + 113) / 2 = 109

90th percentile = 188

Solution:

Step 1. Arrange the data in ascending order: 100, 100, 105, 113, 129, 132, 146, 152, 176, 200

Step 2. Compute the position of the pth percentile (index i):

i = (p / 100) * n), where p = 90 and n = 10

i = (90 / 100) * 10 = 9

Step 3. The index i is an integer ⇒ the 90th percentile is the average of the values in the 8th and 9th positions (176 and 200 respectively)

Answer: the 90th percentile is (176 + 200) / 2 = 188

You might have to round them according to the problem's instructions.