Standard Deviation (SD) is the measure of spread of the numbers in a set of data from its mean value. Also called as SD, Standard Deviations symbol σ (sigma). This can also be said as a measure of variability or volatility in the given set of data.

Find the mean, variance, standard deviation of the given numbers using this free arithmetic standard deviation calculations online.

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Consider a set X of numbers 5,10,15,20,25

**Mean = Sum of X values / N(Number of values) **

= (5+10+15+20+25) / 5

= 75 / 5

= 15

** To find the variance,**

Subtract the mean from each of the values,

5-15 = -10

10-15 = -5

15-15 = 0

20-15 = 5

25-15 = 10

Now square all the answers you have got from subtraction.

(-10)^{2} = 100

(-5)^{2} = 25

(0)^{2} = 0

(5)^{2} = 25

(10)^{2} = 100

Add all the Squared numbers,

100 + 25 + 0 + 25 + 100 = 250

Divide the sum of squares by (n-1)

250 / (5-1) = 250 / 4 = 62.5

Hence Variance = 62.5

**To find the standard deviation**, find the square root of variance,

√62.5 = 7.905

Hence Standard deviation is 7.905

To find minimum and maximum standard deviation,

Minimum SD = Mean - SD

= 15 - 7.905

= 7.094

Maximum SD = Mean + SD

=15 + 7.905

= 22.906

**To find the population standard deviation,**

Divide the sum of squares found in step 2 by n

250 / 5 = 50

Find the square root of 50, √50 = 7.07

This tool will help you dynamically to calculate the statistical problems. Calculating Mean, Variance, Standard deviation is made easier.