A sample is selected from a population with a mean of m 40

A sample is selected from a population with a mean of m = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean a good, representative value for the population?

1.) A small sample and a small population standard deviation

2.) A small sample and a large population standard deviation

3.) A large sample and a small population standard deviation

4.) A large sample and a large population standard deviation

Solution

It is OPTION 2: A small sample and a large population standard deviation.

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As you see, the sample mean is not equal to the population mean.

If the sample is small, then there is a higher chance of getting a sample mean that is not very near the mean, and that is more so when you have a high standard deviation (large variability).