Discussion
Which of the following assertions are CORRECT?
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
Answer: C
The correct assertions are P and R.
- P is true: adding a constant to every entry adds it to the mean.
- Q is false: adding a constant shifts every entry and the mean equally, so the deviations from the mean, and the standard deviation, are unchanged.
- R is true: doubling every entry doubles the mean.
- S is false: doubling every entry doubles every deviation, so the standard deviation doubles.
Every other option includes Q or S, so P, R is the only fully correct choice.
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