Find the mean variance and standard deviation for the following d… - Vidyadip

Question

Find the mean variance and standard deviation for the following data:
$2, 4, 5, 6, 8, 17.$

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Answer

$x$	$d = (x -$ Mean$)$	$d^2$
$2$	$-5$	$25$
$4$	$-3$	$9$
$5$	$-2$	$4$
$6$	$-1$	$1$
$8$	$1$	$1$
$17$	$10$	$100$
$42$		$140$

$\overline{\text{x}}=\frac{1}{\text{n}}\sum\text{x}_\text{i}=\frac{1}{6}[42]=7$
$\text{var}(\text{x})=\frac{1}{\text{n}}\Big\{\sum(\text{x}_\text{i}-\overline{\text{x}})^2\Big\}=\frac{1}{6}\big\{140\big\}=23.33$
$\text{S.D}(\text{x})=\sqrt{\text{var}(\text{x})}=\sqrt{23.33}=4.8$

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