Example 2.18 from Statistics, 2.3 Measures of the Location of the Data

Measures of the Location of the Data: example 2.18

Listed are 29 ages for Academy Award-winning best actors in order from smallest to largest:
18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77

Find the 70^th percentile.
Find the 83^rd percentile.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. - k = 70
  - i = the index
  - n = 29
  i = k100 (n + 1) = (70100)(29 + 1) = 21. This equation tells us that i, or the position of the data value in the data set, is 21. So, we will count over to the 21^st position, which shows a data value of 64.
2. - k = 83^rd percentile
  - i = the index
  - n = 29
  i = k100 (n + 1) = (83100)(29 + 1) = 24.9, which is not an integer. Round it down to 24 and up to 25. The age in the 24^th position is 71, and the age in the 25^th position is 72. Average 71 and 72. The 83^rd percentile is 71.5 years.

How did it go?

Solution

Solution