The mean of the sampling distribution of is equal to the mean of the population.

Hence

= .

Hence, if we take all possible samples (of the same size) from a population and calculate their means, the mean of all these sample means will be the same as the population mean.

The sample mean is called an estimator of the population mean . When the expected value (or mean) of a sample statistic is equal to the value of the corresponding population mean, that sample statistic is said to be an unbiased estimator. For the sample mean , = . Hence, is an unbiased estimator of .

Let us talk about population standard deviation and standard deviation of the sampling distribution of .

First, let us find standard deviation of salaries of five employees.

We will use

to obtain standard deviation of population.

Now let us calculate the value of .

We will use formula

.

We obtain

As we see, the standard deviation of is not equal to the standard deviation of the population distribution. The standard deviation of is equal to the standard deviation of the population divided by the square root of the sample size.

That is,

We also call as a standard error of .

We use the above formula for standard error if the sample size is a small in comparison to the population size. The sample size is considered to be small compared to the population size if the sample size is equal to or less than 5% of the population size, that is, if

If this condition does not satisfied, we use the following formula to

calculate .

The term is often called a finite population correction factor.

In most practical applications, the sample size is usually small compared to the population size.

Consequently, in most cases the formula used for calculating is

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