2019 AMC 12A Problem 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\text{s}, 12 2\text{s}, . . . , 12 28\text{s}, 11 29\text{s}, 11 30\text{s}, and 7 31\text{s}. Let d be the median of the modes. Which of the following statements is true?

\textbf{(A) } \mu < d < M \qquad\textbf{(B) } M < d < \mu \qquad\textbf{(C) } d = M =\mu \qquad\textbf{(D) } d < M < \mu \qquad\textbf{(E) } d < \mu < M

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.