SAT Question 578e26ae: Distributions, Center & Spread answer and explanation with Desmos solution

Choice A is correct. The median is the middle value in a data set when the data are arranged in order from least to greatest. Since there are $15$ values in data set A, the median is the $8$th value. The $8$th value is $23$, so the median of data set A is $23$. The range is found by subtracting the minimum value in a data set from the maximum value. The minimum value in data set A is $22$ and the maximum value is $26$. Therefore, the range of data set A is $26-22$, or $4$. It's given that data set B is created by adding $46$ to each of the values in data set A. Therefore, the $8$th value in data set B is $23+46$, or $69$, so the median of data set B is $69$. The minimum value in data set B is $22+46$, or $68$, and the maximum value is $26+46$, or $72$. Therefore, the range of data set B is $72-68$, or $4$. Since the median of data set A is $23$, and the median of data set B is $69$, the median of data set B is greater than the median of data set A. Since the ranges of data sets A and B are both $4$, the range of data set B is equal to the range of data set A.