Chapter 11, Problem 11SGR

(a)

To determine

To create: The box and whisker plot by using graphing calculator and then describe the shape of the distribution.

Answer to Problem 11SGR

The box and whisker plot by using graphing calculator is shown in figure (1), and the distribution is positively skewed.

Explanation of Solution

Given:

Time in the $400$ meter individual medley is given.

Calculation:

The box and whisker plot is as follows.

  

Figure (1)

The right whisker is longer than the left whisker so the distribution is positively skewed.

Therefore, the box and whisker plot by using graphing calculator is shown in figure (1), and the distribution is positively skewed.

(b)

To determine

To describe: The center and spread of the data using either the mean and standard deviation or the five number summary.

Answer to Problem 11SGR

The median is $311$ , and half of the data are between $307$ and $316$ seconds.

Explanation of Solution

Given:

Time in the $400$ meter individual medley is given.

Calculation:

Since the distribution is skewed, use the five-number summary as shown below.

  

Kelly’s times range from $301$ to $329$ seconds. The median is $311$ , and half of the data are between $307$ and $316$ seconds.