Question

These box plots show the prices for two different brands of shoes.

Answer 1

Answer: Choice C

The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $20.

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Explanation:

Let's go through the answer choices one by one to see which is true and which is false. Also, we'll see which is helpful when it comes to the spread.

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Choice A

The IQR is found by subtracting the values of Q1 and Q3, which are the left and right edges of the box in that order.

For boxplot A, we have an IQR = Q3-Q1 = 80-70 = 10.

So we can immediately rule out choice A because the IQR for boxplot A is not 20, but instead it's 10.

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Choice B

The statement made in choice B is true, since the center vertical lines represent the median, but it's not useful to determine the spread. The median only tells us the center of the distribution. It doesn't tell us how spread out the distribution is.

Imagine you didn't have access to the graph. Now if you're told that the median for brand A is larger than brand B's median, then you'd probably think boxplot A is more spread out; however, the boxplot diagram shows the opposite is the case.

So again the median isn't used here. We can rule out choice B.

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Choice C

This statement is true. We subtract the box edge values to get the IQR values for each boxplot

For brand A we have IQR = Q3-Q1 = 80-70 = 10

For brand B we have IQR = Q3-Q1 = 70-50 = 20

This is the answer we're after.

The IQR is one tool we can use to measure the spread. The range is another option. We could also use the variance or the standard deviation (two slightly similar ideas) to measure the spread.

As you can see from the diagram, the larger the IQR, the more spread out the data will be.

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Choice D

This is false because earlier we've shown 10 is the IQR for brand A.