The variance of the first 10 multiples of 3 i | vedclass

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(C) The first $10$ multiples of $3$ are $3, 6, 9, \ldots, 30$. Let $x_i = 3i$ for $i = 1, 2, \ldots, 10$. The variance $\sigma^2$ is given by $\frac{\

Vedclass · Accepted Answer

$74.25$

Vedclass · Answer

(C) The first $10$ multiples of $3$ are $3, 6, 9, \ldots, 30$. Let $x_i = 3i$ for $i = 1, 2, \ldots, 10$. The variance $\sigma^2$ is given by $\frac{\sum x_i^2}{n} - (\bar{x})^2$. $\bar{x} = \frac{3(1+2+\ldots+10)}{10} = \frac{3 	imes 10 	imes 11}{10 	imes 2} = 16.5$. $\sum x_i^2 = 3^2(1^2+2^2+\ldots+10^2) = 9 	imes \frac{10(11)(21)}{6} = 9 	imes 385 = 3465$. $\sigma^2 = \frac{3465}{10} - (16.5)^2 = 346.5 - 272.25 = 74.25$.

The variance of the first $10$ multiples of $3$ is:

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