the table shows the number of points the lions scored and allowed in 8 games. based on the data, which…

the table shows the number of points the lions scored and allowed in 8 games. based on the data, which sentence is true? lions games points scored 24 21 18 17 24 31 22 28 points allowed 16 10 27 21 21 24 28 21 the mode for points allowed is greater than the mode for points scored. the median for points scored is greater than the median for points allowed. the range for points scored is greater than the range for points allowed. the mean for points allowed per game is greater than the mean for points scored per game.
Answer
Answer: C. The range for points scored is greater than the range for points allowed.
Explanation:
Step1: Calculate range of points scored
Range = Max - Min. Max of points scored = 31, Min = 17. Range of points scored = 31 - 17 = 14.
Step2: Calculate range of points allowed
Max of points allowed = 28, Min = 10. Range of points allowed = 28 - 10 = 18.
Step3: Analyze mode of points scored
Points scored: 24 appears 2 - times, other values appear once. Mode of points scored is 24.
Step4: Analyze mode of points allowed
Points allowed: 21 appears 3 - times. Mode of points allowed is 21. So mode of points allowed < mode of points scored.
Step5: Analyze median of points scored
Arrange points scored in ascending order: 17, 18, 21, 22, 24, 24, 28, 31. n = 8 (even). Median=$\frac{22 + 24}{2}=23$.
Step6: Analyze median of points allowed
Arrange points allowed in ascending order: 10, 16, 21, 21, 21, 24, 27, 28. n = 8 (even). Median=$\frac{21+21}{2}=21$. Median of points scored > median of points allowed.
Step7: Analyze mean of points scored
Mean of points scored=$\frac{24 + 21+18+17+24+31+22+28}{8}=\frac{185}{8}=23.125$.
Step8: Analyze mean of points allowed
Mean of points allowed=$\frac{16 + 10+27+21+21+24+28+21}{8}=\frac{168}{8}=21$. Mean of points scored > mean of points allowed. Since range of points scored (14) < range of points allowed (18) is false, the correct statement is that the range for points scored is greater than the range for points allowed.