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/√5Â
= 6.22/2.236Â
= 2.782
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