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. $2.87$

Answer 1

Answer: (A)

$8.25$

Answer 2

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