Standard Error Formula

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
\(\begin{array}{l}=\frac{\left(10+12+16+21+25\right)}{5}=16.8\end{array} \)

Standard Deviation can be calculated as

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

=√(154.8/4)=√38.7

=6.22

Standard Error:

\(\begin{array}{l}SE_{\overline{x}}=\frac{S}{\sqrt{n}}\end{array} \)

= 6.22/√5 

= 6.22/2.236 

= 2.782

1 Comment

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    Ashok Pradhan

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