SAT Question 608cf8e2: Distributions, Center & Spread answer and explanation with Desmos solution

Choice B is correct. The mean of a data set is the sum of the values divided by the number of values. It's given that a new player earns $18$ points playing the game, and this number of points is added to data set A to create data set B with $51$ values. The histogram shows that all the values in data set A are greater than $18$. Since the additional number of points, $18$, is less than any of the values in the original data set, the mean number of points per player for data set B is less than the mean number of points per player for data set A. The median of a data set with $50$ values is between the $25$th and $26$th values when the values are listed in ascending order. The median of a data set with $51$ values is the $26$th value when the values are listed in ascending order. Therefore, the median of data set B is the $26$th value in data set B, which is the $25$th value in data set A. The histogram shows that the $25$th and $26$th values in data set A are both between $50$ and $60$ points. Therefore, the $25$th and $26$th values in data set A could be equal, in which case the median of data set A would be equal to both the $25$th and $26$th values in data set A. Then, the median number of points per player for data set A would be equal to the median number of points per player for data set B. Therefore, only statement II must be true.