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How to Calculate Standard Deviation ?

Learn how to calculate standard deviation.

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How to Calculate Standard Deviation ?

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  1. HOW TO CALCULATE STANDARD DEVIATION ?

  2. 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.

  3. Standard Deviation

  4. Standard Deviation Calculation • To calculate standard deviation, mean and varaiance shoul be known. • Lets consider an example for simple understanding.

  5. 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

  6. 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

  7. 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.

  8. 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

  9. 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.

  10. Calculate standard deviation online with Standard Deviaton Calculator https://www.easycalculation.com/statistics/standard-deviation.php Thank You!

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