Chapter 11, Problem 8CT

a.

To determine

To draw: A double box-and-whisker plot for the given data.

Explanation of Solution

Given Information: Tables showing the battery lives (in hours) of two brands of laptops is given.

Double box-and-whisker plot:

For brand $A$ ,

Arranging the data in ascending order,

  $8.5,11.5,13.5,13.5,14.5,15.5,16.25,16.75,18.5,20.75$

Lowest value $=8.5$

Highest value $=20.75$

Lower quartile $=13.5$

Upper quartile $=16.75$

Median $=\frac{14.5+15.5}{2}$

     $=15$

For brand $B$ ,

Arranging the data in ascending order,

  $7,8.5,8.5,9,9,9.5,9.75,10.25,10.5,12.5$

Lowest value $=7.8$

Highest value $=12.5$

Lower quartile $=8.5$

Upper quartile $=10.25$

Median $=\frac{9+9.5}{2}$

    $=9.25$

  

b.

To determine

To identify: The shape of each distribution.

Answer to Problem 8CT

For both brands, distribution is skewed right.

Explanation of Solution

Given Information: Tables showing the battery lives (in hours) of two brands of laptops is given.

For Brand $A$ , The median is placed towards the left-side of the box, this means that most of the data lies on left side and distribution is skewed right.

For Brand $B$ ,

The median is placed towards the left-side of the box, this means that most of the data lies on left-side and distribution is skewed right.

c.

To determine

To explain: The battery brand having lives more spread out.

Answer to Problem 8CT

Battery A.

Explanation of Solution

Given Information: Tables showing the battery lives (in hours) of two brands of laptops is given.

Brand $A\text{'}s$ battery lives are more spread out because its range $(20.75-8.5=12.25)$ is greater as compared to brand $B\text{'}s$ battery lives range $(12.5-7=5.5)$ .

d.

To determine

To compare: The distributions using their shapes and appropriate measures of center and variation.

Explanation of Solution

Given Information: Tables showing the battery lives (in hours) of two brands of laptops is given.

As both distributions are skewed, median should be used as a measure of center and five-number summary for measuring variation. For brand $A$ , median is $15$ while for brand $B$ median is $9.25$ .