8. A junior high school sports team needs to purchase a batch of sports shoes to prepare for the school sports meet. It is known that the sports team has 20 students, and the statistical table is as shown in Table 1. Due to an accident, the two data points in the shaded area of Table 1 are no longer visible.
Table 1
\begin{tabular}{|c|c|c|c|c|c|}
\hline Shoe Size & 38 & 39 & 40 & 41 & 42 \\
\hline Number of People & 5 & & & 3 & 2 \\
\hline
\end{tabular}

Which of the following statements is correct? ( ).
(A) The median of this data set is 40, and the mode is 39
(B) The median and mode of this data set must be equal
(C) The mean $P$ of this data set satisfies $39<P<40$
(D) None of the above statements are correct
8.C.
(1) From the meaning of median and mode, as well as Table 1, when the median of this set of data is 40, the mode must be 40. Therefore, option (A) is incorrect.
(2) When the number of people wearing size 39 and size 40 shoes is both 5, the median and mode are not equal, so option (B) is incorrect.
(3) Assuming the remaining 10 people all wear size 39 shoes, the average is 39.35; assuming the remaining 10 people all wear size 40 shoes, the average is 39.85. It can be concluded that option (C) is correct (or by setting the number of people wearing size 39 shoes as $x$, and from $0 \leqslant x \leqslant 10$, the solution can also be obtained).