Question

Give the scores: 88, 64, 77, 94, 67, 59, 99, 87, 94, 71, 75Find the score at the 72nd percentile

Answer 1

The first step in solving for the percentile is to arrange the data set in ascending order, and this now gives us;

`59,64,67,71,75,77,87,88,94,94,99`

Next we rank the numbers from 1 to 11 (since there are 11 numbers altogether in the data set).

`\begin{gathered} 59,64,67,71,75,77,87,88,94,94,99 \\ 1,\text{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} \end{gathered}`

Next we shall apply the following formula;

`R=(P)/(100)(N)`

The variables here are;

`P=\text{percentile,N}=\text{Number of data}`

We now substitute and we have;

`\begin{gathered} R=(72)/(100)(11) \\ R=7.92 \end{gathered}`

We now take the integer part first (that is, 7). Note that between ranks 7 and 8, we have numbers 87 and 88.

The difference between these two numbers is 1, and we now multiply this by the decimal part of the answer earlier derived (that is 0.92) which gives us 0.92. We can now add this back to the integer, which now gives us

`7+0.92=7.92`

This value can be approximated (rounded up) to 8 which means the score at the 72nd percentile is the 8th rank and that is 88.

ANSWER:

The score at the 72nd percentile is 88