Guide on standard error in statistics
Start your free 7-days trial now!
The expected value and variance of the sample mean
Suppose that a random sample of
Note the following points:
these results hold true regardless of the underlying probability distribution of
.only the expected value and variance of the sample mean
can be calculated - not the distribution of .
The expected value of the sample mean is:
The variance of the sample mean is:
Standard error
The standard error is defined as the standard deviation of an estimator or statistic.
Standard error of the sample mean
What is the standard error of the sample mean?
When we try to estimate the population mean using the sample mean, we know that the sample mean won't exactly equal the population mean. In order to know how good the estimate is, we use a statistic called the standard error of the sample mean.
A high value for the standard error means that there is high uncertainty in our estimate, whereas a low standard error means that we can be certain our estimate isn't off by much.
Recall from theorem 5 that the variance of the sample mean
The standard error of the sample mean
As we can see, the standard error decreases as the sample size