Five numbers are 7, 9, $x$, 12 and 15. Their mean is 10.4 and their mode is 9. Find the median.

The five numbers total $5\times 10.4=52$, and 7 + 9 + 12 + 15 = 43, so $x=52-43=9$ — which also makes 9 the only repeated value, agreeing with the given mode. In order the data read 7, 9, 9, 12, 15, so the median is the 3rd value, 9. Here the mean 10.4 sits above the median because the value 15 pulls it up.