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**Comparing Data Displayed in Box Plots**

11.3 Comparing Data Displayed in Box Plots How do you compare two sets of data displayed in box plots?

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ADDITIONAL EXAMPLE 1 The box plots show the distribution of days spent at a national park by two different groups of visitors. A Compare the shapes of the box plots. The position and lengths of the boxes appear to be similar. In both plots, the rightmost whisker is shorter than the leftmost whisker.

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ADDITIONAL EXAMPLE 1 The box plots show the distribution of days spent at a national park by two different groups of visitors. B Compare the centers of the box plots. Group B has a higher median of 3.5, while Group A has a median of 3. This means the median visitor in Group B spends 0.5 day longer at the park.

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ADDITIONAL EXAMPLE 1 The box plots show the distribution of days spent at a national park by two different groups of visitors. C Compare the spreads of the box plots. The box shows the interquartile range, and each box is similar. Group A = 2.25 days; Group B = 2 days. The whiskers are similar lengths, with Group A having slightly more extreme values than Group B.

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ADDITIONAL EXAMPLE 2 The box plots show the distribution of the number of DVDs sold weekly by two different stores. A Compare the shapes of the box plots. The Store B box is longer than Store A, and Store A’s right whisker is much longer.

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ADDITIONAL EXAMPLE 2 The box plots show the distribution of the number of DVDs sold weekly by two different stores. B Compare the centers of the box plots. The Store A box has a median of about 200, and Store B’s median is about 350. Store A’s median is close to Store B’s first quartile, so 50% of Store A’s weekly sales were less than 75% of Store B’s weekly sales.

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ADDITIONAL EXAMPLE 2 The box plots show the distribution of the number of DVDs sold weekly by two different stores. C Compare the spreads of the box plots. Store A: IQR = 150 DVDs; Store B: IQR = 175 DVDs. Store B has a slightly greater interquartile range. Store A has a much longer upper whisker. The position of Store B’s box is higher on the number line, meaning consistently greater DVD sales.

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**11.3 LESSON QUIZ For 1–3, use the box plots. 1.**

7.12.A For 1–3, use the box plots. 1. Compare the shapes of the box plots. The position of Class A is higher, and the ranges of the box plots appear to be very similar.

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For 1–3, use the box plots. 2. Compare the centers of the box plots. The median score for Class A is 10 points higher than for Class B. 3. Compare the spreads of the box plots. The boxes show that the interquartile ranges are similar. Class A has an IQR of 30, and Class B has an IQR of 35. The range of Class A is 70. The range of Class B is 70.

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For 4–6, use the box plots. 4. Compare the shapes of the box plots. The choir’s box is longer than the band’s box, and the band’s right whisker is much longer than the choir’s right whisker. 5. Compare the centers of the box plots. The band has a median of about $200, while the choir has a median of about $350. The choir has 75% of its values greater than the upper quartile of the band’s values.

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For 4–6, use the box plots. 6. Compare the spreads of the box plots. The IQR of the band’s plot is about $100, while the IQR of the choir’s plot is about $150. The position of the choir’s box is much higher on the number line, meaning they earned more money during the fundraiser.

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**How do you compare two sets of data displayed in box plots?**

Sample answer: You can compare the shapes, the centers, and the spreads of the box plots.

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