Exercise 13 Page 367

Consider the given data sets.

Ages of World Cup Winners
$2010$ Men's World Cup Winner (Spain)	$2011$ Women's World Cup Winner (Japan)
$29$ $24$ $23$ $30$ $32$ $26$	$36$ $27$ $24$ $20$ $27$ $23$
$28$ $30$ $26$ $23$ $32$ $28$	$29$ $26$ $25$ $32$ $27$ $27$
$22$ $28$ $24$ $21$ $27$ $22$	$22$ $25$ $24$ $23$ $24$ $28$
$25$ $21$ $24$ $24$ $27$	$20$ $18$ $24$

We will analyze the data and then create a display that best represents the data. A double box-and-whisker plot is one appropriate way to display this quantitative data, since it allows us to compare the distributions of the data sets. To do so, let's write the men's data set in numerical order to find its five-number summary.

From the above we can see that for the men's data set the least value of the data is $21,$ while the greatest value is $32 .$ Additionally, the first quartile is $23,$ the third quartile is $28,$ and the median is $26 .$ In the same way, let's find the five-number summary for the woman's data set.

For the women's data set the least value is $18,$ while the greatest value is $36 .$ The first quartile is $\frac{2 3 + 2 3}{2} = 23,$ the third quartile is $\frac{2 7 + 2 7}{2} = 27,$ and the median is $25 .$ We can now draw a number line that includes the least and greatest value of each data set. Then we will graph points above the number line for the five-number summary.

battery lives double box and whisker plot

Finally, let's draw the box for each plot by using $Q_{1}$ and $Q_{3} .$ Then we will draw a line through the median and the whiskers from the box to the least and greatest values of each data set.

Please note that this is only one possible way to represent the data. However, there are many other possible ways to do it.

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