# The tables show the battery lives (in hours) of two brands of laptops.a) Make a double box-and-whisker plot that represent's the data.

Modeling data distributions
The tables show the battery lives (in hours) of two brands of laptops.

a) Make a double box-and-whisker plot that represent's the data.

b) Identifity the shape of each distribution.

c) Which brand's battery lives are more spread out? Explain.

d) Compare the distributions using their shapes and appropriate measures of center and variation.

2020-12-31
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.