Question

数据集 $[6, 19, 33, 33, 39$ $41, 41, 43, 51, 57]$ 的中位数为 $Q_2 = 40$ 第一四分位数为 $Q_1 = 33$ 第三四分位数为 $Q_3 = 43$ 数据集中的异常值是指比第一四分位数 $(Q_1)$ 低超过四分位距的 $1.5$ 倍，或比第三四分位数 $(Q_3)$ 高超过四分位距的 $1.5$ 倍的值，其中四分位距定义为 $Q_3 - Q_1$ 这个数据集中有多少个异常值？

The data set $[6, 19, 33, 33, 39,$ $41, 41, 43, 51, 57]$ has median $Q_2 = 40,$ first quartile $Q_1 = 33,$ and third quartile $Q_3 = 43.$ An outlier in a data set is a value that is more than $1.5$ times the interquartile range below the first quartile $(Q_1)$ or more than $1.5$ times the interquartile range above the third quartile $(Q_3),$ where the interquartile range is defined as $Q_3 - Q_1.$ How many outliers does this data set have?

$0$

$1$

$2$

$3$

$4$

答案：B

知识点：中位数（数据）

难度评级：1130

解答：

四分位距为 $43 - 33 = 10$ ，它的 $1.5$ 倍是 $15$ 。异常值是小于 $33 - 15 = 18$ 或大于 $43 + 15 = 58$ 的值。只有 $6$ 小于 $18$ ，且没有数大于 $58$ ，所以恰好有 $1$ 个异常值。

所以正确答案是 B。

The interquartile range is $43 - 33 = 10,$ so $1.5$ times it is $15.$ Outliers are values less than $33 - 15 = 18$ or greater than $43 + 15 = 58.$ Only $6$ falls below $18,$ and nothing exceeds $58,$ so there is exactly $1$ outlier.

Thus, the correct answer is B.

2017 AMC 12B 第 5 题

答案：B

难度评级：1130

解答：

其他年份的第 5 题