Standard Error The standard error of a statistic is an estimate of the standard deviation of a statistic. The standard deviation of a statistic describes how a statistic varies from sample to sample. For example, suppose we will take a simple random sample of size 2 from the following population. Population: 1, 3, 4, 5, 7 There are many possible samples, so there are many possible values of the sample mean Y-bar. The table below lists all the possibilities. Sample Y-bar 1, 3 2.0 1, 4 2.5 1, 5 3.0 1, 7 4.0 3, 4 3.5 3, 5 4.0 3, 7 5.0 4, 5 4.5 4, 7 5.5 5, 7 6.0 The standard deviation of Y-bar is the standard deviation of the numbers in the Y-bar column.* The standard deviation tells how Y-bar varies from sample to sample. The nice thing is that we can estimate the standard deviation of Y-bar using only a single sample (which is all we ever get to see in a real problem). For example, suppose we draw the sample Sample: 3, 7 Y-bar = (3+7)/2 = 5 s = sqrt{ [ (3-5)^2 + (7-5)^2 ] / (2-1) } = sqrt(8) The standard error of Y-bar is estimated to be s/sqrt(n)=sqrt(8)/sqrt(2)=2 This is an estimate of the standard deviation of the numbers in the Y-bar column in the table above. *FOOTNOTE The standard deviation of the sample mean is approximately sigma/sqrt(n) if the number of items in the population is much larger than the number of items sampled. In a simple example like this one where the population is very small, the standard deviation of Y-bar won't be sigma/sqrt(n). This is nothing to worry about. The purpose of the example is to help you better understand the standard deviation of a statistic and the standard error of a statistic.