SAT Question d73a67d7: Distributions, Center & Spread answer and explanation with Desmos solution

Choice D is correct. Standard deviation is a measure of the spread of the values in a data set from the mean of the data set, and the smaller the spread, the smaller the standard deviation. Each of the four choices represents a data set that is symmetric with respect to the value $54$. Therefore, $54$ is the mean of each of these data sets. All the values in the data set in choice D differ from $54$ by either $0$ or $1$. In each of the other three data sets, the values in the data set, other than the value of $54$, differ from $54$ by at least $1$. Therefore, the data set in choice D has the smallest spread and thus the smallest standard deviation.