SAT One-variable data: distributions and measures of center and spread Practice Question 4 (Hard) | SAT Owl

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

Math · Problem-Solving and Data AnalysisHard

A data set consists of $11$ positive integers. The median of the data set is $24$ , and the mean is $27$ . If the greatest value in the data set, $80$ , is removed, which of the following must be true?

A

Both the mean and the median stay the same.

B

The mean decreases and the median increases.

C

The mean stays the same and the median decreases.

D

The mean decreases, and the median either decreases or stays the same.

Show answer and explanation

Answer: D

The original sum is $11 \times 27 = 297$ , so the new mean is $\frac{297 - 80}{10} = 21.7$ , a decrease. With $11$ values, the median $24$ is the $6$ th value in order. After removing the greatest value, the new median is the average of the $5$ th and $6$ th original values; since the $5$ th value is at most $24$ , this average is at most $24$ . It equals $24$ only if the $5$ th value is also $24$ .

Choice C is tempting if you think removing one value can't move the mean much, but $80$ is far above the mean, so removing it lowers the mean noticeably.

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