AMC8 2015

AMC8 2015 · Q5

AMC8 2015 · Q5. It mainly tests Arithmetic misc.

Billy's basketball team scored the following points over the course of the first 11 games of the season: 42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73. If his team scores 40 in the 12th game, which of the following statistics will show an increase?

比利的篮球队在前11场比赛中得分如下：42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73。如果第12场比赛得分40，以下哪项统计量会增加？

(A) range 极差

(B) median 中位数

(D) mode 众数

(E) mid-range 中程数

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The range is the high score minus the low score, so the range changes from 31 to 33. The range is the only listed statistic that will increase. Because 40 is the lowest score for the season, it will cause the mean to decrease. The median value of the first 11 games is the 6th highest score, or 58. The median value of the first 12 games will be the average of the 6th highest and 7th highest scores, or $(58+58)/2=58$, so no change will occur in the median. Similarly, the score that occurs most frequently in either situation is 58, so the mode will not change. The mid-range is the average of the highest score and the lowest score. The mid-range of the first 11 games is $(73+42)/2=57.5$. The mid-range of the first 12 games is 56.5, a decrease from 57.5.

答案（A）：极差等于最高分减去最低分，因此极差从 31 变为 33。所列的统计量中，只有极差会增加。因为 40 是该赛季的最低分，它会使平均数降低。前 11 场比赛的中位数是第 6 高的得分，即 58。前 12 场比赛的中位数将是第 6 高与第 7 高得分的平均值，即 $(58+58)/2=58$，因此中位数不会变化。同样，两种情况下出现频率最高的得分都是 58，所以众数不会改变。中程数（mid-range）是最高分与最低分的平均值。前 11 场比赛的中程数是 $(73+42)/2=57.5$。前 12 场比赛的中程数是 56.5，比 57.5 下降了。

Topics

AR.015 Arithmetic misc