Question

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?

$0$

$1$

$2$

$3$

$4$

Solution:

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 Problem 5

Solution:

Problem 5 in Other Years