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2017 AMC 12B Question 5

AMC12 · 2017 AMC 12B

Question 5

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?
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $4$