A statistician collects data from a survey. The data consists of $212$ values. Specifically, the values $1,2,\dots ,20$ each appear $10$ times; the values $21,22$ each appear $5$ times; and the value $23$ appears $2$ times. 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?