Data set A consists of the values 11, 11, 11, 19, 19, 19... | SAT One-variable data: distributions and measures of center and spread Question, Answer Explained

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

Math · Problem-Solving and Data AnalysisHard

Data set A consists of the values $11, 11, 11, 19, 19, 19$ . Data set B consists of the values $11, 13, 15, 15, 17, 19$ . Which of the following statements is true?

A

The two data sets have the same standard deviation because they have the same range.

B

Data set A has a greater mean than data set B.

C

Data set B has a greater standard deviation than data set A.

D

Data set A has a greater standard deviation than data set B.

Show answer and explanation

Answer: D

Both data sets have a mean of $15$ and a range of $19 - 11 = 8$ . Standard deviation measures how far the values typically are from the mean. Every value in data set A is $4$ away from the mean, while the values in data set B are only $0$ , $2$ , or $4$ away. So data set A has the greater standard deviation.

Choice A is tempting because the ranges match, but standard deviation depends on every value, not just the least and greatest.

Why the other choices are wrong

A. The ranges match, but standard deviation depends on every value. All of data set A sits 4 away from the mean.
B. Both data sets have a mean of 15.
C. Data set B has values at 15, right at the mean, so its values are closer to the mean than those in data set A.

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