Question

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. It is added to each number, the variance of the numbers so obtained is 

A. 6.5

B. 2.87 

C. 3.87 

D. 8.25

Answer 1

Consider numbers are 1,2,3,4,5,6,7,8,9,10 

If one is added to each number then, numbers will be 

Let say x_i = 2,3,4,5,6,7,8,9,10,11

 So, N= 10

xi	x2i
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
Σxi = 65	Σx2i = 505

Standard deviation Variance = \(\Big(\frac{\Sigma x^2_i}{N} - \Big(\frac{\Sigma x_i}{N}\Big)^2\Big)\)  

Variance = \(\Big(\frac{505}{10} - \Big(\frac{65}{10}\Big)^2\Big)\)  

Var = 8.25

Hence, the variance is 8.25