Using the given double box-and-whisker plot, determine the percent of the boys and then the percent of the girls who are 66 inches or shorter.
So in this question, we can see two box-and-whisker plots depicting the height of the girls and the boys, with the girls at the top and the box-and-whisker plot for the boys underneath. The figures at the bottom of the diagram represent the height in inches of the girls and the boys. Box-and-whisker plots don’t indicate actual quantities of something. But they give us a general picture for the data. Let’s remind ourselves of how to interpret a box-and-whisker plot.
The lowest point at the end of this first whisker represents the minimum value, in this case, the minimum height. The lowest part of the box represents Q one, also called the lower quartile. It also gives us as a centile the 25th percentile point. The middle line of our box represents Q two or the median. Remembering that our median gives us the value of the data at the halfway point will help us to recall that the percentile here would be 50 percent. The top line at the end of the box represents Q three or the upper quartile and indicates the value at 75 percent. And the last point at the end of our right-hand whisker will represent the maximum value of our data.
In our question, starting with the boys, we need to work out what percentage are 66 inches or shorter. So if we look at the 66 on our number line for the inches, we can see that, on the boys’ box-and-whisker plot, this will fall in at the median point. And we know that this Q two value represents 50 percent. So we can say that 50 percent of the boys are less than 66 inches. And now, if we look at the girls’ box-and-whisker plot, we can see that 66 falls in a different place on this plot. In this case, it will be at Q one, our lower quartile. And since Q one is representative of 25 percent, we can say that 25 percent of the girls are less than 66 inches. Note that if we’d been asked for the percentage of the girls who are 66 inches or more, we would have had to subtract our 25 percent from 100 percent.
Our answer here is that 50 percent of the boys are less than 66 inches. And 25 percent of the girls are less than 66 inches.