Standard Deviation Calculator

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.

Standard Deviation Calculator

To Calculate Mean, Variance, Standard deviation :

Total Numbers
Mean (Average)
Standard deviation
Variance(Standard deviation)
Population Standard deviation
Variance(Population Standard deviation)
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Formula :

Mean : Mean = Sum of X values / N(Number of values) Standard Deviation : standard deviation formula
Population Standard Deviation : population standard deviation formula
Variance : Variance = s2

Example:

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

Step 1 :

Mean = Sum of X values / N(Number of values)
= (5+10+15+20+25) / 5
= 75 / 5
= 15

Step 2 :

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

Step 3 :

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

Step 4 :

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.

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