# Standard Deviation and Mean

take a look at this question:

The sample from Population A has a mean of 35 and a standard deviation of 1. The sample from Population B has a mean of 45 and a standard deviation of 15. Which of the following are certain?

and there is this option:

The average age of Population A is lower than the average age of Population B.

But I can't see why. if population A has SD of just 1 and it mean is 35, how come it can ever have an average population lower than B?

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What is the definition of average age? – gammatester Apr 7 '14 at 11:04
@gammatester I don't have it.. the first part of the question reads as: "You are taking samples of the ages of two populations, A and B. Population A is all the residents of San Francisco, while Population B is all the residents of Los Angeles." – Draconar Apr 7 '14 at 11:09
You could not be certain of this option as you can only make statements about probability like there is a 95% chance that the average age of A is lower than B. To be certain you would have to survey the whole population without error. – user121049 Apr 7 '14 at 11:18

They key word in the question is sample. What this means is that from each of the two populations $A$ and $B$, a subset of individuals were selected from each, and the mean and standard deviations for each population were calculated for these people only.