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AP Statistics/Unit 1: Exploring One-Variable Data
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Effect of Constant Addition on the Mean
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A researcher studying employee salaries computed the mean salary from the data shown above. After giving every employee a $3000 raise, instead of adding $3000 to the original mean, the researcher mistakenly multiplied the original mean by $3000. What is the nature of the mistake made in recalculating the new mean salary? Employee Salary Data ------------------------- | Employee | Salary ($) |
|----------|------------|
| 1 | 3000 |
| 2 | 7000 |
| 3 | 15000 |
| 4 | 22000 |
| 5 | 23000 |
| 6 | 38000 |

A

He recalculated the median instead of the mean after the salary increase.

B

He erroneously multiplied the original mean by the raise amount rather than adding $3000 to the original mean.

C

He properly adjusted the mean but misinterpreted the effect of constant addition on the mean.

D

He subtracted $3000 from each salary, which would lower the overall mean.

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