Question

A comparative box plot for two data sets is shown. Two box-and-whisker plots. The first is titled, Set A, with left whisker 20, right whisker 26, left hand side of box 23.5, right hand side of box 25.5, and median 24. The second is titled, Set B, with left whisker 13, right whisker 23, left hand side of box 14.5, right hand side of box 16.5, and median 15.5. Which statement is true?
More than 25% of the data for each set is greater than 20.

More than 50% of the data for each set is between 20 and 23.

No more than 25% of the data for the sets overlap.

At least 75% of the data is greater than 23.

Answer 1

Answer: Choice C) No more than 25% of the data for the sets overlap

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Explanation:

It sounds like you are given a visual representation of the box plots. However, for reference, I'm going to post an attached image of the plots so we're both on the same page. See the image below.

Figure 1 and Figure 2 both refer to the same set of boxplots. The only difference is that figure 2 has a blue region from x = 20 to x = 23 to show where the two boxplots overlap.

Since this blue region does not contain a full whisker, and only a fraction of one for each plot, this means that less than 25% of the data is overlapping between the two sets. Recall that the distance from the tip of the whisker to the edge of the boxplot represents 25% of the data exactly. The same can be said if you went from the edge of a box (either Q1 or Q3) to the median.