Question

The following are distances (in miles) traveled to the workplace by employees of a certain hospital. 28, 13, 14, 15, 20, 37, 2, 16, 24, 40, 32, 11, 36, 10, 31, 18 Find 25th and 90th percentiles for these distances.

Answer 1

25th percentile of our given data set is 13.

90th percentile of our given data set is 37.

Explanation:

We have been given the distances traveled to the workplace by employees of a certain hospital. 28, 13, 14, 15, 20, 37, 2, 16, 24, 40, 32, 11, 36, 10, 31, 18. We are asked to find 25th and 90th percentile for our given distances.

First of all, we will order our given data in ascending order as:

2, 10, 11, 13, 14, 15, 16, 18, 20, 24, 28, 31, 32, 36, 37, 40

`\text{25th percentile}=(25)/(100)* 16`

`\text{25th percentile}=(1)/(4)* 16`

`\text{25th percentile}=4`

The 25th percentile is 4th data point that is 13, therefore, 25th percentile of our given data set is 13.

`\text{90th percentile}=(90)/(100)* 16`

`\text{90th percentile}=0.9* 16`

`\text{90th percentile}=14.4`

The 90th percentile will be 15th data point that is 37. Therefore, 90th percentile of our given data is 37.