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From the given data we can form the following Table The mean is calculated by step-deviation method taking $14$ as assumed mean. The number of observa

Vedclass · Accepted Answer

$5.74$

Vedclass · Answer

From the given data we can form the following Table The mean is calculated by step-deviation method taking $14$ as assumed mean. The number of observations is $n=10$


	
		
			${x_i}$
			${d_i} = \frac{{{x_i} - 14}}{2}$
			
			Deviations orom mean 

			$\left( {{x_i} - \bar x} ight)$
			
			$\left( {{x_i} - \bar x} ight)$
		
		
			$6$
			$-4$
			$-9$
			$81$
		
		
			$8$
			$-3$
			$-7$
			$49$
		
		
			$10$
			$-2$
			$-5$
			$25$
		
		
			$12$
			$-1$
			$-3$
			$9$
		
		
			$14$
			$0$
			$-1$
			$1$
		
		
			$16$
			$1$
			$1$
			$1$
		
		
			$18$
			$2$
			$3$
			$9$
		
		
			$20$
			$3$
			$5$
			$25$
		
		
			$22$
			$4$
			$7$
			$49$
		
		
			$24$
			$5$
			$9$
			$81$
		
		
			 
			$5$
			 
			$330$
		
	


Therefore    $Mean\,\,\bar x = $ assumed mean $ + \frac{{\sum\limits_{i = 1}^n {{d_i}} }}{n} 	imes h$

$ = 14 + \frac{5}{{10}} 	imes 2 = 15$

and    Veriance $\left( {{\sigma ^2}} ight) = \frac{1}{n}\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - \bar x} ight)}^2} = \frac{1}{{10}} 	imes 330 = 33} $

Thus Standard deviation $\left( \sigma  ight) = \sqrt {33}  = 5.74$

નીચે આપેલ માહિતી માટે વિચરણ શોધો.

$6,8,10,12,14,16,18,20,22,24$

Similar Questions

જો સંખ્યા $-1, 0, 1, k$ નો પ્રમાણિત વિચલન $\sqrt 5$ હોય તો $k$ = ............... ( જ્યાં $k > 0,$)

${x_i}$	${d_i} = \frac{{{x_i} - 14}}{2}$	Deviations orom mean $\left( {{x_i} - \bar x} \right)$	$\left( {{x_i} - \bar x} \right)$
$6$	$-4$	$-9$	$81$
$8$	$-3$	$-7$	$49$
$10$	$-2$	$-5$	$25$
$12$	$-1$	$-3$	$9$
$14$	$0$	$-1$	$1$
$16$	$1$	$1$	$1$
$18$	$2$	$3$	$9$
$20$	$3$	$5$	$25$
$22$	$4$	$7$	$49$
$24$	$5$	$9$	$81$
	$5$		$330$

નીચે આપેલ માહિતી માટે વિચરણ શોધો. $6,8,10,12,14,16,18,20,22,24$

Similar Questions

જો સંખ્યા $-1, 0, 1, k$ નો પ્રમાણિત વિચલન $\sqrt 5$ હોય તો $k$ = ............... ( જ્યાં $k > 0,$)

નીચે આપેલ માહિતી માટે વિચરણ શોધો.

$6,8,10,12,14,16,18,20,22,24$