a)
Double box-and-whisker plot:
For brand A,
Arranging the data in ascending order,
\(\displaystyle{8.5},\ {11.5},\ {13.5},\ {13.5},\ {14.5},\ {15.5},\ {16.25},\ {16.75},\ {18.5},\ {20.75}\)

\(\displaystyle\text{Lowest value}={8.5}\)

\(\displaystyle\text{Highest value}={20.75}\)

\(\displaystyle\text{Lower quartile}={13.5}\)

\(\displaystyle\text{Upper quartile}={16.75}\)

\(\displaystyle\text{Median}={\frac{{{14.5}\ +\ {15.5}}}{{{2}}}}\)

\(\displaystyle={15}\) For brand B, Arranging the data in ascending order, \(\displaystyle{7},\ {8.5},\ {8.5},\ {9},\ {9},\ {9.5},\ {9.75},\ {10.25},\ {12.5}\)

\(\displaystyle\text{Lowest value}={7.8}\)

\(\displaystyle\text{Highest value}={12.5}\)

\(\displaystyle\text{Lower quartile}={8.5}\)

\(\displaystyle\text{Upper quartile}={10.25}\)

\(\displaystyle\text{Median}={\frac{{{9}\ +\ {9.5}}}{{{2}}}}\)

\(\displaystyle={9.25}\) b) 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) Brand A's battery lives are more spread out because its range \(\displaystyle{\left({20.75}\ -\ {8.5}={12.25}\right)}\) is greater as compared to brand B's battery lives range \(\displaystyle{\left({12.5}\ -\ {7}={5.5}\right)}.\) d) 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.

\(\displaystyle\text{Lowest value}={8.5}\)

\(\displaystyle\text{Highest value}={20.75}\)

\(\displaystyle\text{Lower quartile}={13.5}\)

\(\displaystyle\text{Upper quartile}={16.75}\)

\(\displaystyle\text{Median}={\frac{{{14.5}\ +\ {15.5}}}{{{2}}}}\)

\(\displaystyle={15}\) For brand B, Arranging the data in ascending order, \(\displaystyle{7},\ {8.5},\ {8.5},\ {9},\ {9},\ {9.5},\ {9.75},\ {10.25},\ {12.5}\)

\(\displaystyle\text{Lowest value}={7.8}\)

\(\displaystyle\text{Highest value}={12.5}\)

\(\displaystyle\text{Lower quartile}={8.5}\)

\(\displaystyle\text{Upper quartile}={10.25}\)

\(\displaystyle\text{Median}={\frac{{{9}\ +\ {9.5}}}{{{2}}}}\)

\(\displaystyle={9.25}\) b) 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) Brand A's battery lives are more spread out because its range \(\displaystyle{\left({20.75}\ -\ {8.5}={12.25}\right)}\) is greater as compared to brand B's battery lives range \(\displaystyle{\left({12.5}\ -\ {7}={5.5}\right)}.\) d) 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.