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Question:
What is the variance of first 5 natural number?
Answer:

The first 5 natural numbers are: 1, 2, 3, 4, 5

Mean = (1 + 2 + 3 + 4 + 5)/5 = 15/5 = 3

Now, varience = {∑(xi )2 }/n - (Mean)2                  {1 ≤ i ≤ 5}

                   = (12 + 22 + 32 + 42 + 52 )/5 - 32 

                   = (1 + 4 + 9 + 16 + 25)/5 - 9

                   = 55/5 - 9

                   = 11 - 9

                   = 2

So, the varience of the first 5 natural number is 2

Shortcut Method:

The varience of the first n natural number = (n2 - 1)/12

Here, n = 5

So, varience = (52 - 1)/12

                 = (25 - 1)/12

                 = 24/12

                 = 2 

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