Mean and variance for data 6,7,10,12,13,4,8,12

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13.Statistics

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Find the mean and variance for the data $6,7,10,12,13,4,8,12$

A

$9.25$

B

$9.25$

C

$9.25$

D

$9.25$

Solution

$6,7,10,12,13,4,8,12$

Mean, $\bar x = \frac{{\sum\limits_{i = 1}^8 {{x_i}} }}{n}$

$=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}=9$

The following table is obtained

${x_i}$	$\left( {{x_i} – \bar x} \right)$	${\left( {{x_i} – \bar x} \right)^2}$
$6$	$-3$	$9$
$7$	$-2$	$4$
$10$	$-1$	$1$
$12$	$3$	$9$
$13$	$4$	$16$
$4$	$-5$	$25$
$8$	$-1$	$1$
$12$	$3$	$9$
		$74$

Variance $\left( {{\sigma ^2}} \right) = \frac{1}{n}\sum\limits_{i = 1}^8 {{{\left( {{x_i} – \bar x} \right)}^2} = \frac{1}{8} \times 74} = 9.25$

Standard 11

Mathematics

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