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. Well, standard errors and standard deviations are similar. Although we cannot use these terms interchangeably. Standard deviation refers to the uncertainty in a random variable or data set, whereas SE refers to the uncertainty of an estimator. This distinction is important because the general error of an estimator declines as the sample size increases. Meanwhile, the standard deviation does not change with the sample size.
Standard glitches are critical in hypothesis testing and when performing Monte Carlo simulations. In both applications, the general glitch indicates the accuracy of the estimate.

Example of Standard Glitch:

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

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

Why is standard error important?

Every inferential statistic has a general error associated with it. The general error is an important statistic that offers information about its accuracy. Even if we do not report it always.