SAT Question c178d4da: Distributions, Center & Spread answer and explanation with Desmos solution

Choice A is correct. The mean value of a data set is the sum of the values of the data set divided by the number of values in the data set. When a data set is represented in a frequency table, the sum of the values in the data set is the sum of the products of each value and its frequency. For data set A, the sum of products of each value and its frequency is $30\left(2\right)+34\left(4\right)+38\left(5\right)+42\left(7\right)+46\left(9\right)$, or $1,094$. It's given that there are $27$ values in data set A. Therefore, the mean of data set A is $\frac{1,094}{27}$, or approximately $40.52$. Similarly, the mean of data B is $\frac{958}{27}$, or approximately $35.48$. Therefore, the mean of data set A is greater than the mean of data set B.