SAT Question 4626102e: Distributions, Center & Spread answer and explanation with Desmos solution

Choice C is correct. The median of a data set with an odd number of values, in ascending or descending order, is the middle value of the data set, and the range of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in ascending order and there are $15$ values in the data set, the eighth value in data set A, $23$, is the median. The maximum value in data set A is $26$ and the minimum value is $22$, so the range of data set A is $26-22$, or $4$. It's given that data set B is created by adding $56$ to each of the values in data set A. Increasing each of the $15$ values in data set A by $56$ will also increase its median value by $56$ making the median of data set B $79$. Increasing each value of data set A by $56$ does not change the range, since the maximum value of data set B is $26+56$, or $82$, and the minimum value is $22+56$, or $78$, making the range of data set B $82-78$, or $4$. Therefore, the median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.