Raj polled 100 students in his class to compare the number of hours that teen boys and girls played video games each week. The results of his survey are shown below. Which gender shows greater variability in their playing time?

Hours of Video Game Time per Week for Teen Boys
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 9 to 17. A line divides the box at 14.5.

Hours of Video Game Time per Week for Teen Girls
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 3 to 15. A line divides the box at 6.
Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.

Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.

Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.

Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.

It may depend on conditions. The dispersion can be measured in many ways. We can find range (max value - min. value), or interquartile range(the absolute difference between the first and third quartile ), etc to measure the variability.

How does a boxplot shows the data points?

A box plot has 5 data description.

The leftmost whisker shows the minimum value in the data.
The rightmost whisker shows the maximum value in the data.
The leftmost line in the box shows the first quartile.
The middle line shows the median, also called second quartile.
The last line of the box shows the third quartile.

How to find the interquartile range?

IQR(inter quartile range) is the dfference between third and first quartile.

We will use the interquartile range here to find the variability in the playing time taken by different genders.

From the box plots given, we get the data of first and third quartiles from the left and right limits of boxes.

For males (teen boys):

First quartile: left limit of box = 9
Third quartile: right limit of box = 17

IQR is 17-9 = 8

For females (teen girls):

First quartile: left limit of box = 3
Third quartile: right limit of box =15

IQR is 15-3 = 12

Thus, there is greater variability in playing time of teen girls (females).

Thus, the gender that shows greater variability in their playing time is females (teen girls).

Learn more about box-plot here:

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