AMC12 2017 B

AMC12 2017 B · Q5

AMC12 2017 B · Q5. It mainly tests Arithmetic misc.

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?

数据集 $[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]$ 的中位数 $Q_2 = 40$，第一四分位数 $Q_1 = 33$，第三四分位数 $Q_3 = 43$。数据集中离群值是低于第一四分位数 ($Q_1$) 1.5 倍四分位距的值，或高于第三四分位数 ($Q_3$) 1.5 倍四分位距的值，其中四分位距定义为 $Q_3 - Q_1$。这个数据集有多少个离群值？

(A) 0 0

(B) 1 1

(D) 3 3

(E) 4 4

Answer

Correct choice: (B)

正确答案：（B）

Solution

Because 1.5 times the interquartile range for this data set is $1.5\cdot(43-33) = 15$, outliers are data values less than $33-15 = 18$ or greater than $43 + 15 = 58$. Only the value 6 meets this condition, so there is 1 outlier.

因为该数据集的 1.5 倍四分位距为 $1.5\cdot(43-33) = 15$，离群值是小于 $33-15 = 18$ 或大于 $43 + 15 = 58$ 的数据值。只有值 6 满足此条件，因此有 1 个离群值。

Topics

AR.015 Arithmetic misc