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Step-by-step explanation:
The "mean" of a sample is the sum the sampled values divided by the number of items in the sample:
For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is
The variance is calculated as follows:
S2=∑(Xi-X)/(N-1)
The standard deviation is calculated as follows:
For example the standard deviation is the square root from the variance and in this case for the five values: 4, 36, 45, 50, 75 is to be calculated as:
N=5 and the mean for x= 42
Xi
Xi-X
(Xi-X)2
4
-38
1444
36
-6
36
45
3
9
50
8
64
75
33
1089
∑Xi= 210
∑(Xi-X)2= 2642
In this case the variance is 2642/4 =660.5 and the standard deviation is √2642/5= 32.5
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