Question 663·Hard·Math

With ten values, the median is halfway between the fifth and sixth values in order. If the missing integer is greater than $14$, those positions hold $11$ and $13$. They're equally far from $12$, so the median would be $12$. That tells you where the missing integer could go, but not its exact value.

The mean is the total divided by the count, so multiply the mean by the count to recover the total. Calling the total $T$:

Type the nine given integers as a list named $a$, then type $\operatorname{total}(a)$. Desmos prints $99$, the sum of the nine known values.

Let $x$ be the one missing integer. Its value plus the known sum must equal the total for all ten:

The difference belongs to one integer, so don't divide it by ten again.

Type $\operatorname{total}(a)+x_1\sim150$. Desmos uses $x_1$ for the unknown and $\sim$ to find its value; under PARAMETERS, it shows $x_1=51$. Because $51$ is greater than $20$, it goes last, is distinct from the other integers, and leaves $11$ and $13$ in the middle as checked earlier. The remaining integer is $51$. Grid in 51.