Answer: The percentile that corresponds to an age of 36 years old in the given data set is approximately 22.22%.
Explanation:
To find the percentile that corresponds to an age of 36 years old in a data set representing the ages of 36 executives, we can use the following steps:
Step 1: Arrange the data set in ascending order.
- Let's assume the data set is as follows (in ascending order): 28, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63.
Step 2: Calculate the rank of the given age.
- The rank is the position of the given age within the data set.
- In this case, the given age is 36 years old, and its rank is 8 because it is the 8th value in the data set.
Step 3: Calculate the percentile using the rank and the total number of data points.
- The percentile can be calculated using the following formula:
Percentile = (Rank / Total number of data points) x 100
- In this case, the total number of data points is 36 (since there are 36 executives' ages in the data set).
- Plugging in the values, we get:
Percentile = (8 / 36) x 100
Percentile ≈ 22.22 (rounded to two decimal places)