Standard Deviation Calculator

Standard deviation is a measure of spread of numbers in a set of data from its mean value. Use our online standard deviation calculator to find the mean, variance and arithmetic standard deviation of the given numbers.

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

Standard deviation is a measure of spread of numbers in a set of data from its mean value. Use our online standard deviation calculator to find the mean, variance and arithmetic standard deviation of the given numbers.

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Formula :

Mean : Mean = Sum of X values / N(Number of Values)
Variance : Variance = s2
Sample Standard Deviation : Standard Deviation Formula
Population SD : Population Standard Deviation Formula

In statistics, Standard Deviation (SD) is the measure of 'Dispersement' of the numbers in a set of data from its mean value. This is represented using the symbol σ (sigma). The formula for the Standard Deviation is square root of the Variance. Here is a free online arithmetic standard deviation calculator to help you solve your statistical questions. This can also be used as a measure of variability or volatility for the given set of data. Enter the set of values in the online SD calculator to calculate the mean, standard deviation, variance and population standard deviation.

Example:

Consider a set X = {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 Hence Mean = 15

Step 2 :

To find the variance,
Subtract the mean from each of the x 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 :

Find the square root of variance,
√62.5 = 7.905
Hence Standard deviation is 7.905

To find minimum and maximum SD,
Minimum SD = Mean - SD
= 15 - 7.905
= 7.094

Maximum SD = Mean + SD
=15 + 7.905
= 22.906

Step 4 :

To find the population SD,
Divide the sum of squares found in step 2 by n
250 / 5 = 50
Find the square root of 50, √50 = 7.07

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