SAT Question bf47ad54: Distributions, Center & Spread answer and explanation with Desmos solution

Choice A is correct. The tables in choices B, C, and D each represent a data set where the values $80$ and $90$ have the same frequency and the values $70$ and $100$ have the same frequency. It follows that each of these data sets is symmetric around the value halfway between $80$ and $90$, or $85$. When a data set is symmetric around a value, that value is the mean of the data set. Therefore, the data sets represented by the tables in choices B, C, and D each have a mean of $85$. The table in choice A represents a data set where the value $90$ has a greater frequency than the value $80$ and the value $100$ has a greater frequency than the value $70$. It follows that this data set has a mean greater than $85$. Therefore, of the given choices, choice A represents the data set with the greatest mean.