Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is

Question

Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is (A) 8.25 (B) 6.5 (C) 3.87 (D) 2.87

Tardigrade Admin · Accepted Answer

Variance of first 10 natural numbers =(102-1/12) = 8.25. On multiplying by - 1, variance is multiplied by (-1)2 and it does not change, when a constant quantity is added to each item.

Q. Consider the first $10$ positive integers. If we multiply each number by $- 1$ and then add $1$ to each number, the variance of the numbers so obtained is

$8.25$

$6.5$

$3.87$

$2.87$

Variance of first 10 natural numbers $= \frac{1 0 ^{2} - 1}{12}$
$= 8.25$ . On multiplying by $- 1$ , variance is multiplied by $(- 1)^{2}$ and it does not change, when a constant quantity is added to each item.

Q. Consider the first 10 positive integers. If we multiply each number by −1 and then add 1 to each number, the variance of the numbers so obtained is

8.25

6.5

3.87

2.87