# Standard Error Calculator

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):

Population St. Dev. ($$\sigma$$)
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 $$se$$.

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