### CFA Practice Question

Which of the following is (are) true?

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.

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