A data set has mean and standard deviation . Every value is multiplied by and then is added. What are the new mean and standard deviation?
Answer and explanation
Correct answer: D. Mean , standard deviation
- Step 1: The mean transforms like the data: . Step 2. The standard deviation is multiplied by and is not changed by adding : . **Answer: Mean , standard deviation . Why not the others:** Mean , standard deviation : Adding does not change the spread. Mean , standard deviation : The mean must also be shifted by . Mean , standard deviation : Multiplying by doubles the standard deviation.
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