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.
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
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
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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