Answer to Question #335739 in Statistics and Probability for Nanda

Question

Find the percentile rank of the 18 using the following data: 15, 13, 6, 5, 12, 22, 50, 18

Answer 1

In order to compute the corresponding percentile rank for $X = 18,$ the data needs to be organized into ascending order, as shown in the table below

$$\def\arraystretch{1.5} \begin{array}{c:c} Position & X (Asc. Order) \\ \hline 1 & 5 \\ \hdashline 2 & 6 \\ \hdashline 3 & 12 \\ \hdashline 4 & 13 \\ \hdashline 5 & 15 \\ \hdashline 6 & 18 \\ \hdashline 7 & 22 \\ \hdashline 8 & 50 \\ \hdashline \end{array}$$

Let $k$ be the number of values in the dataset that are less than $X = 18.$

In this case, $k = 5.$ Hence, the percentile rank is:

$$Percentile \ Rank=\dfrac{k}{n}=\dfrac{5}{8}=0.625$$

Percentile Rank $=62.5\%.$