16Hit1600
Problem-Solving and Data AnalysisHardScaling every value in a data set

Problem-Solving and Data Analysis practice question

Every value in a data set is multiplied by 3 to form a new data set. Which of the following statements about the new data set is true?

  1. A. Its mean and its standard deviation are both 3 times those of the original data set.Correct
  2. B. Its mean is 3 times the original mean, but its standard deviation is unchanged.
  3. C. Its mean is unchanged, but its standard deviation is 3 times the original.
  4. D. Its mean and its standard deviation are both unchanged.

Answer: A. Its mean and its standard deviation are both 3 times those of the original data set.

Multiplying every value by 3 triples the mean. It also triples every gap between values, and the standard deviation measures those gaps, so it triples too. (ADDING a constant would shift the mean and leave the spread alone.)

Why the other answers are wrong

B. Its mean is 3 times the original mean, but its standard deviation is unchanged.
That is what happens when a constant is ADDED to every value. Multiplying stretches the spread as well.
C. Its mean is unchanged, but its standard deviation is 3 times the original.
Tripling every value certainly changes the mean — it triples.
D. Its mean and its standard deviation are both unchanged.
Both change: the values are all three times larger and three times more spread out.

More Problem-Solving and Data Analysis questions

Not affiliated with the College Board. SAT is a trademark of the College Board.