Question

Given the following data find the diameter that represents the 38th percentile

Answer 1

Here are the steps in determining the nth percentile.

1. Arrange the data set from the lowest to the highest value.

`\begin{gathered} 1.31,1.33,1.34,1.35,1.36 \\ 1.37,1.42,1.53,1.53,1.54 \\ 1.55,1.58,1.58,1.61,1.67 \end{gathered}`

2. Divide the nth percentile by 100 and multiply the result by the number of data in the set.

`38/100=0.38`
`0.38*15=5.7`

3. Round the result to the nearest whole number.

`5.7\approx6`

4. Count the 6th data in the data set starting from the lowest. In the arranged data set, the 6th value is 1.37.

Hence, 1.37 is the diameter that represents the 38th percentile.