Question 575·Medium·Math

No Desmos needed. A matching shift in the dot plots answers both comparisons directly. In each dot plot, a stack’s height counts students. A’s stacks at $3,4,5,6,7,8$ have heights $1,2,4,3,1,1$. B has those same heights at $13,14,15,16,17,18$. So every B page count is its A counterpart plus $10$.

The mean is the page total divided by the number of students. Since every count increases by $10$ and the number of students stays the same, B’s mean is A’s mean plus $10$. You don’t need to calculate either mean separately.

Standard deviation measures spread around a club’s own mean. Let $x$ be any count in A and $m$ be A’s mean. The matching count in B is $x+10$, and B’s mean is $m+10$. Subtract each mean from its count:

So every count stays the same distance from its own mean. Adding the same amount to every value moves the mean but leaves standard deviation unchanged. B’s mean is $10$ pages greater than A’s, and their standard deviations are equal. Choice A.