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# What is Standard Error?

## What is a Standard Error?

The standard deviation of the mean (or any other estimator) is known as a standard error. Standard errors and standard deviations are similar, although these terms are not used interchangeably. Standard deviation refers to the uncertainty in a random variable or data set, whereas standard error refers to the uncertainty of an estimator. This distinction is important because the standard error of an estimator declines as the sample size increases. Meanwhile, the standard deviation does not change with the sample size.
Standard errors are critical in hypothesis testing and when performing Monte Carlo simulations. In both applications, the standard error indicates the accuracy of the estimate.

## Example of Standard Error:

$SE\, =\, \frac{\sigma }{\sqrt{n}}$

where,
σ = standard deviation
n = no. of observations

## Why is standard error important?

Every inferential statistic has a standard error associated with it. The standard error is an important statistic that offers information about its accuracy, even if it isn’t always reported.

Owais Siddiqui
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