A data set has a standard deviation of . Every value is multiplied by , and then is added to each result. What is the standard deviation of the new data set?
Answer and explanation
Correct answer: D.
- Step 1: For a linear transformation , the standard deviation transforms as .
- Step 2: Adding a constant shifts the data without affecting dispersion, while multiplying by scales the standard deviation by : .
Answer
.
Why not the others: erroneously adds to the scaled standard deviation (); uses ; adds ; computes .
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