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2019 AMC 12A Question 7

AMC12 · 2019 AMC 12A

Question 7

Melanie computes the mean $\mu,$ the median $M,$ and the modes of the $365$ values that are the dates in the months of $2019.$ Thus her data consist of $12$ $1$s, $12$ $2$s, $\ldots,$ $12$ $28$s, $11$ $29$s, $11$ $30$s, and $7$ $31$s. Let $d$ be the median of the modes. Which of the following statements is true?
  1. $\mu \lt d \lt M$
  2. $M \lt d \lt \mu$
  3. $d = M = \mu$
  4. $d \lt M \lt \mu$
  5. $d \lt \mu \lt M$