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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.
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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.
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The figures at the bottom of the diagram represent the height in inches of the girls and the boys.
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Box-and-whisker plots don’t indicate actual quantities of something.
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But they give us a general picture for the data.
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Let’s remind ourselves of how to interpret a box-and-whisker plot.
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The lowest point at the end of this first whisker represents the minimum value, in this case, the minimum height.
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The lowest part of the box represents Q one, also called the lower quartile.
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It also gives us as a centile the 25th percentile point.
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The middle line of our box represents Q two or the median.
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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.
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The top line at the end of the box represents Q three or the upper quartile and indicates the value at 75 percent.
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And the last point at the end of our right-hand whisker will represent the maximum value of our data.
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In our question, starting with the boys, we need to work out what percentage are 66 inches or shorter.
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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.
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And we know that this Q two value represents 50 percent.
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So we can say that 50 percent of the boys are less than 66 inches.
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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.
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In this case, it will be at Q one, our lower quartile.
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And since Q one is representative of 25 percent, we can say that 25 percent of the girls are less than 66 inches.
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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.
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Our answer here is that 50 percent of the boys are less than 66 inches.
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And 25 percent of the girls are less than 66 inches.