**Instructions:** This standard error calculator allows you to compute a standard error, showing all the steps. Please provide the population standard deviation (σ) and the sample size (n):

## More About the Standard Error

The standard error \(se\) corresponds to the standard deviation of the sample mean. Let us recall that if we take a sample \(X_1\), \(X_2\), …, \(X_n\), in which each each \(X_i\) is a random variable with population standard deviation \(\sigma\), the the sample mean

\[ \bar X = \sum_{i=1}^n X_i\]is also a random variable, with a standard deviation equal to \(\frac{\sigma}{\sqrt n}\). This standard deviation of the sampling distribution of sample mean is called the *standard error* \(se\).