Question

Find 25th and 90th persontiles for these agesAnswer a & b

Answer 1

Arrange the data in ascending order

`27,32,33,35,37,38,39,39,42,42,44,44,45,46,54,60,60,62`

QUESTION A

There are 18 values in the data.

The percentile rank is calculated using the formula:

`r=(p)/(100)\cdot(n+1)`

For the question, we have the following parameters:

`\begin{gathered} p=25 \\ n=18 \end{gathered}`

Therefore, the rank is:

`\begin{gathered} r=(25)/(100)(18+1)=(1)/(4)(19) \\ r=4.75 \end{gathered}`

Since the rank is not an integer, round up to the nearest integer. Hence the rank is 5.

The 5th number is 37.

Hence, the 25th percentile is 37.

QUESTION B

Following the method above, the rank is calculated to be:

`\begin{gathered} p=90 \\ \therefore \\ r=(90)/(100)(19)=17.1 \end{gathered}`

To the nearest integer, the rank is 17.

The 17th number is 60.

The 90th percentile is 60.