આપેલ પ્રત્યેક માહિતી માટે મધ્યક અને વિચરણ શોધો :

${x_i}$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

${f_i}$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

Question

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\

Vedclass · Accepted Answer

Vedclass · Answer

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.


	
		
			${x_i}$
			$\left( {{x_i} - \bar x} ight)$
			${\left( {{x_i} - \bar x} ight)^2}$
		
		
			$3$
			$-13.5$
			$182.25$
		
		
			$6$
			$-10.5$
			$110.25$
		
		
			$9$
			$-7.5$
			$56.25$
		
		
			$12$
			$-4.5$
			$20.25$
		
		
			$15$
			$-1.5$
			$2.25$
		
		
			$18$
			$1.5$
			$2.25$
		
		
			$21$
			$4.5$
			$20.25$
		
		
			$24$
			$7.5$
			$56.25$
		
		
			$27$
			$10.5$
			$110.25$
		
		
			$30$
			$13.5$
			$182.25$
		
	


Variance  $\left( {{\sigma ^2}} ight) = \frac{1}{n}\sum\limits_{i = 1}^{10} {{{\left( {{x_1} - \bar x} ight)}^2} = } \frac{1}{{10}} 	imes 742.5 = 74.25$

$742.5$

વર્ગ	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
આવૃત્તિ	$5$	$8$	$15$	$16$	$6$

$\mathrm{x}$	$\mathrm{x}_{1}=2$	$\mathrm{x}_{2}=6$	$\mathrm{x}_{3}=8$	$\mathrm{x}_{4}=9$
$\mathrm{f}$	$4$	$4$	$\alpha$	$\beta$

આપેલ પ્રત્યેક માહિતી માટે મધ્યક અને વિચરણ શોધો : ત્રણના પ્રથમ $10$ ગુણિત

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