Chapter 5, Problem 27E

a)

To determine

To find the median winning speed.

Answer to Problem 27E

Median is 36.2.

Explanation of Solution

Given:

  

Calculation:

An estimated median is the intersection of the vertical line with horizontal axis with horizontal line at 50 on the vertical axis.

  

Hence, the median = 36.2.

b)

To determine

To find the quartiles.

Answer to Problem 27E

Quartile 1 is 35 and quartile 3 is 36.8.

Explanation of Solution

Given:

  

Calculation:

First we have to find Quartile 1. So, need to draw a horizontal line at 25 on the vertical axis. Then take intersection of the vertical line with horizontal axis.

  

An estimated $Q_1\approx 35$

Follow the same procedure for quartile 3 just draw a horizontal line at 75 on the vertical axis.

An estimated $Q_3\approx 36.8$

c)

To determine

To estimate range and IQR.

Answer to Problem 27E

An estimated Range is 7 and IQR is 1.8

Explanation of Solution

Given:

  

Quartile 1 is 35 and quartile 3 is 36.8.

Formula:

  $\begin{array}{l}Range=Highestvalue-Lowestvalue\\ IQR=Q_3-Q_1\end{array}$

Calculation:

Using formula,

  $\begin{array}{l}Range=38-31=7\\ IQR=36.8-35=1.8\end{array}$

d)

To determine

To create a boxplot.

Explanation of Solution

Given:

  

Quartile 1 is 35 and quartile 3 is 36.8.

Calculation:

The boxplot is,

  

e)

To determine

To explain the boxplot.

Explanation of Solution

Given:

  

  

The shape of the distribution is left-skewed. The center is around 36.2. The spread of the distribution is between 31 and 38 mph. There are no outliers for the given data.