Which statement correctly compares the standard deviations of the two sets?

Question

Two data sets each have 5 values and the same mean of 50.
Set A: 48, 49, 50, 51, 52
Set B: 30, 40, 50, 60, 70

Accepted Answer

B. Set B has the larger standard deviation.. Standard deviation measures spread around the mean. Both sets share the mean 50, but Set B's values lie much farther from 50 than Set A's, so Set B has the larger standard deviation. On the SAT you compare spread by inspection, not by computing; the trap is thinking exact calculation is required (choice D).

Answer

A. Set A has the larger standard deviation. — Set A's values sit within 2 of the mean while Set B's stretch 20 away from it, so Set A is the tighter, less spread-out set — smaller standard deviation, not larger.

Answer

C. The standard deviations are equal. — Equal means do not imply equal spread; standard deviation measures distance from the mean, and Set B's distances (up to 20) dwarf Set A's (up to 2).

Answer

D. The standard deviation cannot be compared without calculating it exactly. — You can compare spread by inspection here — Set B's values are visibly much farther from 50 than Set A's, so no computation is needed.

Problem-Solving and Data Analysis practice question

Answer: B. Set B has the larger standard deviation.

Why the other answers are wrong

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