

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
