The five numbers 8, 12, $x$, 20, 26 are written in ascending order, and the mean of the five equals their median. Find $x$.

With five values in order the median is the middle one, $x$. The mean is $(8+12+x+20+26)/5=(66+x)/5$, so $(66+x)/5=x$ gives $66+x=5x$, that is $4x=66$ and $x=16.5$ — which lies between 12 and 20, so the list really is in ascending order. The value 13.2 = 66/5 is the mean of the other four numbers and forgets that $x$ counts in the mean as well; 22 = 66/3 divides by the wrong count; and 16 is merely the halfway point of 12 and 20.