Arrange the data in ascending order
[tex]27,32,33,35,37,38,39,39,42,42,44,44,45,46,54,60,60,62[/tex]
QUESTION A
There are 18 values in the data.
The percentile rank is calculated using the formula:
[tex]r=\frac{p}{100}\cdot(n+1)[/tex]
For the question, we have the following parameters:
[tex]\begin{gathered} p=25 \\ n=18 \end{gathered}[/tex]
Therefore, the rank is:
[tex]\begin{gathered} r=\frac{25}{100}(18+1)=\frac{1}{4}(19) \\ r=4.75 \end{gathered}[/tex]
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:
[tex]\begin{gathered} p=90 \\ \therefore \\ r=\frac{90}{100}(19)=17.1 \end{gathered}[/tex]
To the nearest integer, the rank is 17.
The 17th number is 60.
The 90th percentile is 60.
