# 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

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

=âˆš(154.8/4)=âˆš38.7

=6.22

Standard Error:

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

= 6.22/âˆš5Â

= 6.22/2.236Â

= 2.782