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Standard Error Formula

Standard error is an important statistical measure and it is concerned with standard deviation. The accuracy of a sample that represents a population is knows through this formula. The sample mean deviates from the population and that deviation is called standard error formula.

\[\large SE_{\overline{x}}=\frac{S}{\sqrt{n}}\]

s is the standard deviation
n is the number of observation

Solved example

Question: Calculate the standard error of the given data:
x: 10, 12, 16, 21, 25


Mean $=\frac{\left(10+12+16+21+25\right)}{5}=16.8$ 

Standard Deviation can be calculated as


$=\sqrt{\frac{2167.2}{4}} = 5.418$

Standard Error:



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