Standard Error of the Mean

For times where we can only get a sample (like political polls), we can exploit the third aspect of the Central Limit Theorem:

The variance of the sample means will be close to the variance of the population, divided by the sample size.

This allows us to calculate the Standard Error of the Mean (SEM or SE).

$SE=\frac{\sigma }{\sqrt{n}}$ Where:

• $\sigma$: Standard deviation of the population
• $n$, size of the sample

However, this requires us to calculate the standard deviation of the population, which is not always possible. In cases, we can use the standard deviation of the sample, if that’s all we got.