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.