The mean weight of 5 packages is 12 pounds. When a sixth... | 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 AnalysisMedium

The mean weight of $5$ packages is $12$ pounds. When a sixth package is added, the mean weight of the $6$ packages is $13$ pounds. What is the weight, in pounds, of the sixth package?

$1$

$13$

$14$

$18$

Show answer and explanation

Answer: D

The $5$ packages weigh a total of $5 \times 12 = 60$ pounds. The $6$ packages weigh a total of $6 \times 13 = 78$ pounds. So the sixth package weighs $78 - 60 = 18$ pounds.

Choice C assumes the new mean is the average of the old mean and the new weight, $\frac{12 + 14}{2} = 13$ , but the old mean stands for $5$ packages, not $1$ .

Why the other choices are wrong

A. 1 is the change in the mean, not the weight of the sixth package.
B. 13 is the new mean. A package that weighed 13 pounds would raise the mean to only about 12.17.
C. This treats the new mean as the average of 12 and the new weight, but the old mean stands for 5 packages.

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