Question

1. the stem and leaf plot shows the average points - per - game in the nba playoffs, rounded to the nearest whole point, for two different nba basketball players, michael jordan and lebron james. which of the following statements is true? michael jordan lebron james 2|3 4 9 2|5 5 6 6 7 8 8 9 2 2 1 1 1 3|0 0 1 3 4 7 6 6 5 5 5 3|5 4|4 average points per playoff game key: 4|4 = 44 a) the median of the average points - per - game for jordan is less than the median of the average points - per - game for james. b) the range of the average points - per - game for jordan is less than the range of the average points - per - game for james. c) the interquartile range is the same for both players. d) the mean of the average points - per - game for jordan is less than the median of the average points - per - game for james. e) both distributions are skewed to the right.

Explanation:

Step1: List Jordan's data

Jordan's data: 29, 31, 31, 32, 32, 35, 35, 35, 36, 36, 37, 44

Step2: Calculate Jordan's median

There are 12 data - points. Median is the average of 6th and 7th ordered values. Median of Jordan's data = $\frac{35 + 35}{2}=35$

Step3: Calculate Jordan's range

Range = Max - Min. Max = 44, Min = 29. Range of Jordan's data = 44 - 29 = 15

Step4: Calculate Jordan's quartiles

Q1 is the median of the lower half. Lower half: 29, 31, 31, 32, 32, 35. Q1 = $\frac{31+32}{2}=31.5$. Q3 is the median of the upper half. Upper half: 35, 35, 36, 36, 37, 44. Q3 = $\frac{36 + 36}{2}=36$. Inter - quartile range (IQR) = Q3 - Q1 = 36 - 31.5 = 4.5

Step5: List James's data

James's data: 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 33, 34, 35

Step6: Calculate James's median

There are 16 data - points. Median is the average of 8th and 9th ordered values. Median of James's data = $\frac{28+29}{2}=28.5$

Step7: Calculate James's range

Max = 35, Min = 23. Range of James's data = 35 - 23 = 12

Step8: Calculate James's quartiles

Q1 is the median of the lower half. Lower half: 23, 24, 25, 25, 26, 26, 27, 28. Q1 = $\frac{25+26}{2}=25.5$. Q3 is the median of the upper half. Upper half: 29, 30, 30, 31, 33, 34, 35. Q3 = $\frac{30+31}{2}=30.5$. Inter - quartile range (IQR) = Q3 - Q1 = 30.5 - 25.5 = 5

Step9: Analyze option A

Median of Jordan (35) > Median of James (28.5), so option A is false.

Step10: Analyze option B

Range of Jordan (15) > Range of James (12), so option B is false.

Step11: Analyze option C

Jordan's IQR = 4.5, James's IQR = 5, so option C is false.

Step12: Analyze option D

Mean of Jordan's data: $\bar{x}=\frac{29 + 31+31+32+32+35+35+35+36+36+37+44}{12}=\frac{403}{12}\approx33.58$. Median of James's data = 28.5. Mean of Jordan > Median of James, so option D is false.

Step13: Analyze option E

For Jordan, most of the data is in the 30 - 35 range with a few larger values (44), skewed right. For James, most of the data is in the 20 - 30 range with a few larger values (33, 34, 35), skewed right. So option E is true.

Answer:

E. Both distributions are skewed to the right.