Standard Deviation Calculator

Standard Deviation (SD) is the measure of spread of the numbers in a set of data from its mean value. It is also called as SD and is represented using the 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 and SD of the given numbers using this free arithmetic standard deviation calculator online. Enter an 'n' number of values in the calculator and find the SD (σ), mean and variance.

Standard Deviation Calculator

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)
Variance : Variance = s2
Sample Standard Deviation : Standard Deviation Formula
Population SD : Population Standard Deviation Formula

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 :

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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