Every value of a data set is increased by 5. Which statement about the standard deviation and the mean is correct?

Answer and explanation

Correct answer: B. The mean increases by 5 and the standard deviation does not change

  1. Step 1: A shift moves all values equally, so their average also moves by 5. Step 2. The spread, measured by the distance from the mean, does not change. **Answer: mean , standard deviation unchanged. Why not the others:** Only scaling (multiplying) changes the standard deviation, and a shift does not.

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