The mean of 8 quiz scores is 82. A teacher then discovers... | 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 of $8$ quiz scores is $82$ . A teacher then discovers that one score was recorded as $64$ when it should have been $84$ . After the score is corrected, what is the mean of the $8$ quiz scores?

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Answer: 84.5

The original sum is $8 \times 82 = 656$ . Correcting the score adds $84 - 64 = 20$ to the sum, so the new sum is $676$ . The new mean is $\frac{676}{8} = 84.5$ .

Adding the full $20$ points to the mean gives $102$ , but the $20$ points are shared across all $8$ scores, so the mean rises by only $\frac{20}{8} = 2.5$ .

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