The variance of the first 10 natural numbers | vedclass

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(D) The first $10$ natural numbers that are multiples of $3$ are: $3, 6, 9, 12, 15, 18, 21, 24, 27, 30$.The mean $\mu$ is calculated as: $\mu = \frac{

Vedclass · Accepted Answer

$74.25$

Vedclass · Answer

(D) The first $10$ natural numbers that are multiples of $3$ are: $3, 6, 9, 12, 15, 18, 21, 24, 27, 30$.The mean $\mu$ is calculated as: $\mu = \frac{3+6+9+12+15+18+21+24+27+30}{10} = \frac{165}{10} = 16.5$.The variance $\sigma^2$ is given by the formula $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2$.Calculating the sum of squares of deviations: $\sum (x_i - 16.5)^2 = (3-16.5)^2 + (6-16.5)^2 + \dots + (30-16.5)^2 = 182.25 + 110.25 + 56.25 + 20.25 + 2.25 + 2.25 + 20.25 + 56.25 + 110.25 + 182.25 = 742.5$.Therefore,$\sigma^2 = \frac{742.5}{10} = 74.25$.

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
$f_i$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

The variance of the first $10$ natural numbers which are multiples of $3$ is

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