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2019 AMC 10A Question 12

AMC10 · 2019 AMC 10A

Question 12

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 $12$ copies of $1,$ $12$ copies of $2,$ and so on through $12$ copies of $28,$ then $11$ copies of $29,$ $11$ copies of $30,$ and $7$ copies of $31.$ 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. $d \lt \mu \lt M$