Difficult# An Equal Mode and Median

SATMAT-XTGJVE

The least and greatest integers in a list of nine integers are $ 3 $ and $ 13 $ respectively. The mean of these nine integers is $ 8 $, and the number $ 4 $ occurs twice in the list. In this list, the integer, $ m $, is both the median and the mode.

Which of the following is a true statement about the value for $ m $?