HOW TO CALCULATE STANDARD DEVIATION ?

Standard Deviation

• The measure of how much the data is spread out form the mean is called as standard deviation.

• It is expresses in sigma.

• The higher the dispersion, the higher standard deviation.

Standard Deviation

Standard Deviation Calculation

• To calculate standard deviation, mean and varaiance shoul be known.

• Lets consider an example for simple understanding.

Standard Deviation ExampleMeasure the height of all the person's in your home.

If your home contains four members and their height's are :

A = 165

B = 145

C = 153

D = 150

Standard Deviation - Mean

Now you have to find the mean of the heights measured.

Mean is nothing but average.

Mean = 165 + 145 + 153 + 150

4

= 500.5

Standard Deviation - Variance

Next step is to find the variance.

It is the average of the squares of the differences from mean.

Subtract individual heights from the mean and square each value.

Standard Deviation - VarianceA = (165 - 153.25) = (11.75)^2 = 138.0625

B = (145 - 153.25) = (-8.25)^2 = 68.0625

C = (153 - 153.25) = (-0.25)^2 = 0.0625

D = (150 - 153.25) = (-3.25)^2 = 10.5625

Variance = 138.0625 + 68.0625+0.0625+10.5625

4 - 1

= 72.25

Standard DeviationNow Standard Deviation = Square root (Variance)

= Square root ( 72.25)

= 8.5

For population standard deviation, we would calculate variance without subtracting 1 from the denominator.

Thank You!Calculate standard deviation online with

Standard Deviaton Calculator

https://www.easycalculation.com/statistics/standard-deviation.php