A data set has mean and standard deviation . Each value is multiplied by , and then is subtracted. What are the new mean and standard deviation?
Answer and explanation
Correct answer: C. mean , standard deviation
- Step 1: The mean transforms like each value: .
- Step 2: Multiplying by scales the standard deviation by : .
- Step 3: Subtracting shifts every value equally and does not change the spread.
Answer
mean , standard deviation .
Why not the others: The option subtracts from the spread; ignores the subtraction; a standard deviation of ignores the multiplication.
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