A survey recorded the number of books read by participants in a month. The frequencies are as follows: values $1$ through $5$ appear $5$ times each; values $6$ through $10$ appear $10$ times each; values $11$ through $15$ appear $12$ times each; values $16$ through $20$ appear $10$ times each; and values $21$ through $25$ appear $5$ times each. Let $\mu$ be the mean, $M$ be the median, and $d$ be the median of the modes of this data set. Which of the following statements is true?