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Standard Error Calculator
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Standard error calculator helps to find out the standard error of the given population. It is mentioned as the standard deviation of sampling distribution. The mathematical formula to find out the standard error is given below.

$SE_{x}$=$\frac{S}{\sqrt{n}}$

Where $SE_{x}$ is the standard error
S is the sample standard deviation
n is the number of observations

## Steps for Standard Error Calculator

Step 1 :

Write down the given observations after reading the question.

Step 2 :

Find out the mean of the data using the following equation.

$\mu$ =$\frac{x_{1}+x_{2}+.......+x_{n}}{n}$

Step 3 :

Using the mean value calculate the sample standard deviation. The formula used for this will be,

S=$\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\mu )^{2}}$

Step 4 :

Then the standard error is given by,

$SE_{x}$=$\frac{S}{\sqrt{n}}$

## Problems on Standard Error Calculator

1. ### Determine the standard error of the following.3,5,7,9

Step 1 :

The given observations are,

3,5,7,9

Step 2 :

Mean $\mu$ is given by,

$\mu$ =$\frac{x_{1}+x_{2}+.......+x_{n}}{n}$

$\mu$ =$\frac{3+5+7+9}{4}$

$\mu$ =$\frac{24}{4}$=6

Step 3 :

Sample standard deviation is

S=$\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\mu )^{2}}$

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=(3-6)2+(5-6)2+(7-6)2+(9-6)2

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=9+1+1+9=20

S=$\sqrt{\frac{1}{4-1}×20}$=2.5819

Step 4 :

The standard error is given by,

$SE_{x}$=$\frac{S}{\sqrt{n}}$

$SE_{x}$=$\frac{2.5819}{\sqrt{4}}$=1.2909

$SE_{x}$=1.2909

2. ### Calculate the standard error of the given data15,20,25

Step 1 :

The given observations are,

15,20,25

Step 2 :

Mean $\mu$ is given by,

$\mu$ =$\frac{x_{1}+x_{2}+.......+x_{n}}{n}$

$\mu$ =$\frac{15+20+25}{3}$

$\mu$ =$\frac{60}{3}$=20

Step 3 :

Sample standard deviation is

S=$\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\mu )^{2}}$

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=(15-20)2+(20-20)2+(25-20)2

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=25+25=50

S=$\sqrt{\frac{1}{3-1}×50}$=5

Step 4 :

The standard error is given by,

$SE_{x}$=$\frac{S}{\sqrt{n}}$

$SE_{x}$=$\frac{5}{\sqrt{3}}$=2.8867

$SE_{x}$=2.8867

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