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**CFA Practice Question**

Which of the following is (are) true?

II. Adding a constant to each value in a sample leaves the mean unchanged.

III. The mean of a sample decreases as the number of observations increases.

I. Doubling every single value in a sample doubles the sample mean.

II. Adding a constant to each value in a sample leaves the mean unchanged.

III. The mean of a sample decreases as the number of observations increases.

A. I only.

B. I and II.

C. II and III.

**Explanation:**Adding a constant to each value in a sample increases the mean by the same constant. III is incorrect. As the number of observations increases, it is the expected difference between the sample mean and the population mean that decreases.

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**User Contributed Comments**
7

User |
Comment |
---|---|

sivenkova |
is 1 really true? There seems to be an error in the formulating... |

mc01 |
try it using two numbers and you will indeed realize that it is true. |

Kuki |
"As the number of observations increases, it is the expected difference between the sample mean and the population mean that decreases." What does this mean? |

Kuki |
aahh...no worries...i figured it out... |

MaximeL |
what if 1 of the number of the sample is negative? (-1 x2 +1 x2)/2 = 0 (1+1)/2 = 1 |

dybacis |
MaximeL you forgot to use -1 in your secodn equitaion. Your original values are -1 and 1, the mean is 0, if you multiply by 2 they will become -2 and 2 so mean is 0 or 2*0 |

dybacis |
and that is what happens when I type too fast, I wish there was en edit comment function |