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

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

=√(154.8/4)=√38.7

=6.22

Standard Error:

\(SE_{\overline{x}}=\frac{S}{\sqrt{n}}\)

= 6.22/√5 

= 6.22/2.236 

= 2.782

1 Comment

  1. byjus is a site not only for learning but also for enhancing the knowledge.
    Appreciate for creating such a site. Keep it and wish you all the very best.
    Ashok Pradhan

Leave a Comment Cancel reply

Your email address will not be published. Required fields are marked *