SAT One-variable data: distributions and measures of center and spread Practice Question 2 (Hard) | SAT Owl

Question bank / One-variable data: distributions and measures of center and spread

Math · Problem-Solving and Data AnalysisHard

A data set has a mean of $12$ and a standard deviation of $4$ . Each value in the data set is multiplied by $3$ , and then $5$ is subtracted from each result. What are the mean and standard deviation of the new data set?

A

Mean $31$ , standard deviation $7$

B

Mean $36$ , standard deviation $12$

C

Mean $31$ , standard deviation $4$

D

Mean $31$ , standard deviation $12$

Show answer and explanation

Answer: D

Applying the same operations to every value applies them to the mean: $3(12) - 5 = 31$ . Multiplying every value by $3$ triples the distances between values, so the standard deviation becomes $3(4) = 12$ . Subtracting $5$ from every value shifts the data without changing its spread, so the standard deviation stays $12$ .

Choice A applies the subtraction to the standard deviation, but shifting every value by the same amount does not change spread.

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