SAT Question 457d2f2c: Distributions, Center & Spread answer and explanation with Desmos solution

Choice D is correct. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the middle value. Out of the $27$ different numbers in this data set, $13$ numbers are below the median, one number is exactly $33$, and $13$ numbers are above the median. When $7$ is subtracted from each number below the median and added to each number above the median, the data spread out from the median. Since the median of this data set, $33$, is equivalent to the mean of the data set, the data also spread out from the mean. Since standard deviation is a measure of how spread out the data are from the mean, a greater spread from the mean indicates an increased standard deviation.