Which Average Should the Coach Report?
A basketball coach records the points scored by her team over 11 games: 48, 52, 55, 55, 58, 60, 61, 64, 70, 72, 145. The 145 came from a double-overtime game. A reporter asks for "the typical score." The coach computes the mean and the median. She also notices the team's scores are skewed by that one outlier game. She must decide which measure to quote and be able to justify it.
1. Compute the mean and the median of the 11 scores.
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Sum = 48+52+55+55+58+60+61+64+70+72+145. Group: (48+52)=100; (55+55)=110; (58+60)=118; (61+64)=125; (70+72)=142; +145. 100+110+118+125+142+145 = 740. Mean = 740 ÷ 11 ≈ 67.3 (67.27...). Median: 11 values already in order, the middle is the 6th value = 60. So mean ≈ 67.3, median = 60.
2. Which measure better represents a "typical" score, and how much does the outlier pull the mean? Quantify the effect.
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The median (60) is the better "typical" value: 10 of 11 games are between 48 and 72, and the median sits inside that cluster. The mean (67.3) is pulled upward by the single 145 game. Quantify: replace 145 with a value near the cluster, say 72 (the next highest). New sum = 740 − 145 + 72 = 667; new mean = 667 ÷ 11 ≈ 60.6, close to the median. So the single overtime game inflates the mean by roughly 67.3 − 60.6 ≈ 6.7 points. The median barely moves with one extreme value, which is why it is the defensible choice here.