Every value in a data set is multiplied by and then is added. The original mean is and the original standard deviation is . What are the new mean and standard deviation?
Answer and explanation
Correct answer: B. mean and standard deviation
- Step 1: The mean is transformed in the same way as each value: .
- Step 2: Adding shifts every value equally, so the spread is unchanged by it.
- Step 3: Multiplying by stretches the spread by a factor of , so the standard deviation is .
Answer
mean and standard deviation .
Why not the others: mean and standard deviation : adds the constant to the spread, but a shift does not change the spread. mean and standard deviation : ignores the multiplication when finding the spread. mean and standard deviation : forgets that the mean shifts when is added.
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