How to calculate standard deviation
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Learn how to calculate standard deviation.

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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 calculation
Standard Deviation Calculation

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

  • Lets consider an example for simple understanding.


Standard deviation example
Standard Deviation Example

  • Measure 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
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
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 variance1
Standard Deviation - Variance

  • A = (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 deviation2
Standard Deviation

  • Now 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.


Calculate standard deviation online with Standard Deviaton Calculator

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

Thank You!


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