SAT Question 881ef5f5: Distributions, Center & Spread answer and explanation with Desmos solution

Any nine consecutive integers can be written as $k$, $k+1$, $k+2$, $k+3$, $k+4$, $k+5$, $k+6$, $k+7$, $k+8$. The mean of the integers is their sum divided by $9$: $\frac{k+k+1+k+2+\cdots +k+8}{9}=\frac{9k+36}{9}$, which simplifies to $k+4$. So $a=k+4$. Since there is an odd number of integers (nine), the median is the integer in the middle when all the integers are ordered from least to greatest: $k+4$. So $b=k+4$. Therefore, $|a-b|=|(k+4)-(k+4)|$, which is $0$.