Questions: Emma, Sally, and Olivia play for the school basketball team. The dot plots show the number of points each of them scored in 20 games. Find the interquartile range, IQR, for each dot plot. Then, place the basketball players in order from greatest to least IQR.

Emma, Sally, and Olivia play for the school basketball team. The dot plots show the number of points each of them scored in 20 games. Find the interquartile range, IQR, for each dot plot. Then, place the basketball players in order from greatest to least IQR.
Transcript text: Emma, Sally, and Olivia play for the school basketball team. The dot plots show the number of points each of them scored in 20 games. Find the interquartile range, IQR, for each dot plot. Then, place the basketball players in order from greatest to least IQR.
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Solution

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Solution Steps

Step 1: Find the IQR for Emma

First, we list Emma's points in increasing order: 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 14. There are 20 data points. The median is the average of the 10th and 11th data points, which is (11+11)/2 = 11. The first quartile (Q1) is the median of the first 10 data points, which is (9+10)/2 = 9.5. The third quartile (Q3) is the median of the last 10 data points, which is (11+12)/2 = 11.5. The IQR for Emma is Q3 - Q1 = 11.5 - 9.5 = 2.

Step 2: Find the IQR for Sally

Sally's points in increasing order are: 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14. There are 20 data points. The median is the average of the 10th and 11th data points, which is (10+11)/2 = 10.5. The first quartile (Q1) is the median of the first 10 data points, which is (8+9)/2 = 8.5. The third quartile (Q3) is the median of the last 10 data points, which is (12+13)/2 = 12.5. The IQR for Sally is Q3 - Q1 = 12.5 - 8.5 = 4.

Step 3: Find the IQR for Olivia

Olivia's points in increasing order are: 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13. There are 20 data points. The median is the average of the 10th and 11th data points, which is (10+10)/2 = 10. The first quartile (Q1) is the median of the first 10 data points, which is (9+9)/2 = 9. The third quartile (Q3) is the median of the last 10 data points, which is (11+12)/2 = 11.5. The IQR for Olivia is Q3 - Q1 = 11.5 - 9 = 2.5.

Final Answer

Sally > Olivia > Emma \( \boxed{\text{Sally} > \text{Olivia} > \text{Emma}} \)

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