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  4. 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

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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

Statistics

Solution:

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.