Question

the day of the lowest show the most ever in a single day by random sample of 13 students calculate the 38th and the 60th percentile of data

Answer 1

We have that the sample consist in n=13 students. The percentile formula is given by

$P_x=\frac{x}{100}\times n\text{ position}$

where x denotes the percentaje. In the first case, p=38, then, we have

$\begin{gathered} P_{38}=\frac{38}{100}\times13\text{ position} \\ P_{38}=4.94\text{ position} \end{gathered}$

then, we get

$P_{38}=41$

that is, P_38 corresponds to 41 miles driven.

In the second case, by substituting x=60 in our formula, we get

$\begin{gathered} P_{60}=\frac{60}{100}\times13\text{ position} \\ P_{60}=7.8\text{ position} \end{gathered}$

which gives

$P_{60}=56$

that is, P_60 corresponds to 56 miles driven.

Then, the answers are:

$P_{38}=41$

This means that approximately 38% of the data lie below 41, when the data are ranked.

$P_{60}=56$

This means that approximately 60% of the data lie below 56, when the data are ranked.