Question

The two box-and-whisker plots below represent the distribution of shoe sizes for a group of 40 two-year-old boys and a group of 80 three-year-old boys.
What is the difference of the interquartile ranges of the box-and-whisker plots?

0
0.5
1
1.5

Answer 1

Answer: Choice B)  0.5

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Explanation:

For now, focus solely on the orange boxplot. The first quartile Q1 is the left edge of the box, which is at 3.5; while the value of Q3 is 7.5 (right edge of the box). The interquarile range (IQR) is ...

IQR = Q3 - Q1

IQR = 7.5 - 3.5

IQR = 4

This is basically the width of the box. Ignore the whiskers when it comes to the IQR.

Let A = 4 as we'll use it later.

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Find the IQR for the blue box plot

Q1 = 6 = left edge of the blue box

Q3 = 9.5 = right edge of the blue box

IQR = Q3 - Q1

IQR = 9.5 - 6

IQR = 3.5

Let B = 3.5 as we'll use it later

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Subtract the values of A and B to find the difference of the IQR values

A - B = 4 - 3.5 = 0.5