Chapter 7.2, Problem 21E

(a)

To determine

To explain:

The range and interquartile range of the given data.

Explanation of Solution

Given:

The data set

Concept used:

The median is the middle number in a sorted ascending or descending list of numbers and more descriptive of that data set than the average.

Calculation:

The first quartile denoted by $Q_1$ is the median of the lower half of the data set.

Order the data and the median of the lower half.

The difference of the greatest value and the least value of the data set is different.

Both brand A and brand B are skewed right and most of the data are on the left side of the plot

(b)

To determine

To find:

The range and interquartile range of the given data.

Answer to Problem 21E

  $2.5,3.5$

Explanation of Solution

Given:

The data set

Concept used:

The median is the middle number in a sorted ascending or descending list of numbers and more descriptive of that data set than the average.

Calculation:

The first quartile denoted by $Q_1$ is the median of the lower half of the data set.

Order the data and the median of the lower half.

The difference of the greatest value and the least value of the data set is different

Since the range of the upper $75\%$ data set is the difference of the greatest value

Brand A

  $\begin{array}{l}=7-3.5\\ =3.5\end{array}$

Brand B

  $\begin{array}{l}=5.75-3.25\\ =2.5\end{array}$

(c)

To determine

To describe:

The distribution of the given data.

Answer to Problem 21E

  $1.25,1$

Explanation of Solution

Given:

The data set

Concept used:

The median is the middle number in a sorted ascending or descending list of numbers and more descriptive of that data set than the average.

Calculation:

The first quartile denoted by $Q_1$ is the median of the lower half of the data set.

Order the data and the median of the lower half.

The other $3$ asks for the interquartile range

The difference of $Q_{3}and{Q}_1$

Brand A

  $\begin{array}{l}=4.75-3.5\\ =1.25\end{array}$

Brand B

  $\begin{array}{l}=4.25-3.25\\ =1\end{array}$

The interquartile range of brand A is greater than the interquartile range of brand B.

(d)

To determine

To explain:

The data more spread out between $Q_{1}and{Q}_2$ or $Q_{2}and{Q}_3$ of the given data.

Answer to Problem 21E

Brand A the data is more spread out.

Explanation of Solution

Given:

The data set

Concept used:

The median is the middle number in a sorted ascending or descending list of numbers and more descriptive of that data set than the average.

Calculation:

The first quartile denoted by $Q_1$ is the median of the lower half of the data set.

Order the data and the median of the lower half.

The difference of the greatest value and the least value of the data set is different

Brand A

  $\begin{array}{l}=7-3.5\\ =3.5\end{array}$

Brand B

  $\begin{array}{l}=5.75-3.25\\ =2.5\end{array}$

The difference of $Q_{3}and{Q}_1$

Brand A

  $\begin{array}{l}=4.75-3.5\\ =1.25\end{array}$

Brand B

  $\begin{array}{l}=4.25-3.25\\ =1\end{array}$

So,brand A the data is more spread out.

(e)

To determine

To explain:

The range and interquartile range of the given data.

Explanation of Solution

Given:

The data set

Concept used:

The median is the middle number in a sorted ascending or descending list of numbers and more descriptive of that data set than the average.

Calculation:

The first quartile denoted by $Q_1$ is the median of the lower half of the data set.

Order the data and the median of the lower half.

The difference of the greatest value and the least value of the data set is different.

Both brand A and brand B are skewed right and most of the data are on the left side of the plot

Brand A

The battery life vary by no more than $3.5$ hours