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 \(\sigma\), then 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 \(s_e\).

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