Question

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

• A. 2.87
• B. 8.25
• C. 6.5
• D. 3.87

Answer 1

The correct option is B 8.25

If each observation is increased by 'a'

where 𝑎,$ϵR$ then the variance remains unchanged.

Hence, if 1 is added to each number 1 to 10,

Variance is same as of 1 to 10. Variance of first 𝑛 natural numbers, where 𝑛 is even is

Variance ${\sigma }^2=\frac{n^2-1}{12}$

For n=10,

Variance $=\frac{{10}^2-1}{12}$

Variance $=\frac{99}{12}$

Variance $=8.25$

Hence, option (D) is correct