Question

Given the following data, find the percentile of an age of 52 years: Ages of Presidents (in years): 49, 51, 60, 51, 62, 45, 44, 65, 47, 45, 46, 65, 65, 54, 61, 68, 61, 57, 63, 68 a) 30th percentile b) 45th percentile c) 55th percentile d) 70th percentile

Answer 1

b) 45th percentile

Explanation:

To find the percentile of a given data point in a set of data, we first need to arrange the data in ascending order, then determine the position of the data point in the sorted data set.

Here's the sorted list of ages:

44, 45, 45, 46, 47, 49, 51, 51, 52, 54, 57, 60, 61, 61, 62, 63, 65, 65, 65, 68, 68

The formula to calculate the percentile of a score (age in this case) is:

`Percentile = (Rank of the score / Total numbers in the data) * 100`

Let's find the rank of the age 52:

The rank of 52 is 9 (it's the 9th number in the sorted list). There are 21 total ages, so let's plug these into the percentile formula:

Percentile for age 52: `(9 / 21) * 100 ≈ 42.857 `

So, the age of 52 is approximately in the 43rd percentile. Therefore, out of the options given (30th, 45th, 55th, 70th), the best choice would be:

b) 45th percentile

Hope this helps! :)