Question

Listed are $29$ages for Academy Award winning best actors in order from smallest to largest. $18;21;22;25;26;27;29;30;31;33;36;37;41;42;47;52;55;57;58;62;64;67;69;71;72;73;74;76;77$a. Find the ${40}^{th}$ percentile.

b. Find the ${78}^{th}$ percentile.

Short answer

a. ${40}^{th}$percentile is $37years.$

b.${78}^{th}$percentile is$70years.$

Step-by-step solution

Content Introduction

Consider the given $29$ages for AA winning best actors ordered from smallest to largest. The $k^{th}$percentile is calculated as:

$i=\frac{k}{100}(n+1)$

Here, $i$ is the position of data values,$n$is total number of data values.

Step : Explanation (Part a)

The ${40}^{th}$percentile is calculated as:

$$\begin{gathered} i=\frac{k}{100}(n+1) \\ i=\frac{40}{100}(29+1) \\ i=12 \end{gathered}$$

Here,$12$is an integer and data value of${12}^{th}$position in given ordered data set is$37.$

Explanation (Part b)

The ${78}^{th}$percentile is calculated as follow:

$$\begin{gathered} i=\frac{k}{100}(n+1) \\ i=\frac{78}{100}(29+1) \\ i=23.4 \end{gathered}$$

Here, $23.4$is not an integer. Round it down to$23and24$. You will get$70$.