Find the mean and variance for the first $10$ multiples of $3$

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The first $10$ multiples of $3$ are

$3,6,9,12,15,18,21,24,27,30$

Here, number of observations, $n=10$

Mean,  $\bar x = \frac{{\sum\limits_{i = 1}^{10} {{x_i}} }}{{10}} = \frac{{165}}{{10}} = 16.5$

The following table is obtained.

${x_i}$ $\left( {{x_i} - \bar x} \right)$ ${\left( {{x_i} - \bar x} \right)^2}$
$3$ $-13.5$ $182.25$
$6$ $-10.5$ $110.25$
$9$ $-7.5$ $56.25$
$12$ $-4.5$ $20.25$
$15$ $-1.5$ $2.25$
$18$ $1.5$ $2.25$
$21$ $4.5$ $20.25$
$24$ $7.5$ $56.25$
$27$ $10.5$ $110.25$
$30$ $13.5$ $182.25$

Variance  $\left( {{\sigma ^2}} \right) = \frac{1}{n}\sum\limits_{i = 1}^{10} {{{\left( {{x_1} - \bar x} \right)}^2} = } \frac{1}{{10}} \times 742.5 = 74.25$

$742.5$

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