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.

S E_{\overset{―}{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{(10 + 12 + 16 + 21 + 25)}{5} = 16.8 \end{array}

Standard Deviation can be calculated as

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

=√(154.8/4)=√38.7

=6.22

Standard Error:

\begin{array}{l} S E_{\overset{―}{x}} = \frac{S}{\sqrt{n}} \end{array}

= 6.22/√5

= 6.22/2.236

= 2.782

Standard Error Formula

Solved example

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