SAT One-variable data: distributions and measures of center and spread Practice Question 11 (Hard) | SAT Owl

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

Math · Problem-Solving and Data AnalysisHard

A data set of $15$ values has a mean of $40$ and a standard deviation of $6$ . A new value of $40$ is added to the data set. Which of the following describes the effect on the mean and standard deviation?

A

The mean stays the same, and the standard deviation increases.

B

The mean stays the same, and the standard deviation decreases.

C

The mean increases, and the standard deviation stays the same.

D

Both the mean and the standard deviation stay the same.

Show answer and explanation

Answer: B

Adding a value equal to the mean leaves the sum of $16$ values equal to $16 \times 40$ , so the mean stays $40$ . The new value is $0$ units from the mean, so it adds no spread but increases the number of values. The typical distance from the mean shrinks, so the standard deviation decreases.

Choice D is tempting because the new value matches the mean, but adding a value with no deviation dilutes the spread and lowers the standard deviation.

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