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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.

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

Where,
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

Solution:

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

Standard Deviation can be calculated as

$\sqrt{\frac{1}{4}}\left(10-16.8\right)^{2}+\left(12-16.8\right)^{2}+\left(16-16.8\right)^{2}+\left(21-16.8\right)^{2}+\left(25-16.8\right)^{2}$

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

Standard Error:

$SE_{\overline{x}}=\frac{S}{\sqrt{n}}$

$=\frac{5.418}{\sqrt{5}}=2.42$

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