SAT Question 8736334b: Distributions, Center & Spread answer and explanation with Desmos solution

Choice C is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is $\frac{72+73+73+76+76}{5}$, which simplifies to $74$. The mean of data set B is represented by the equation $\frac{61+64+74+85+x}{5}$, or $\frac{284+x}{5}$. It's given that the mean of data set A is equal to the mean of data set B. Therefore, the equation $74=\frac{284+x}{5}$ can be used to solve for $x$. Multiplying both sides of this equation by $5$ yields $370=284+x$. Subtracting $284$ from both sides of this equation yields $86=x$.