Standard Error Definition

The standard error of an estimation is the estimated standard deviation of the error in the estimation. Specifically, it estimates the standard deviation of the difference between estimated values and the true values.

Notice that the true value of the standard deviation in a population is usually unknown and the use of the term standard error  carries with it the idea that an estimate of this unknown quantity is being used. It also carries with it the idea that it measures, not the standard deviation of the estimate itself, but the standard deviation of the error in the estimate, and these can be very different.

SE_bar{x} = frac{s}{sqrt{n}}

where

s is the sample standard deviation (i.e., the sample based estimate of the standard deviation of the population), and
n is the size (number of items) of the sample.

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