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Illustration of Standard Deviation
The less spread out the numbers are, therefore smaller the standard deviation will be, as it is a way of determining the spread of the data. Similarly, the more spread out the numbers are, the bigger the standard deviation will be. For illustration here are two data sets which have similar number of values and also the similar mean, but the standard deviations are quite dissimilar:
>> x1 = [9 10 9.4 9.6];
>> mean(x1)
ans =
9.5000
>> std(x1)
0.4163
>> x2 = [2 17 -1.5 20.5];
>> mean(x2)
>> std(x2)
10.8704
Illustration of Variance For illustration, for the vector [4, 6, 1, 5], there are n = 4 values therefore n - 1 is 3. The mean of this data set is also 4. The variance will be
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