ટૂંકી રીતનો ઉપયોગ કરીને મધ્યક અને પ્રમાણિત વિ | vedclass

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Question

The data is obtained in tabular form as follows.


	
		
			${x_i}$
			${f_i}$
			${f_i} = \frac{{{x_i} - 64}}{1}$
			${y_i}^2$
			${f_i}{y_i}

Vedclass · Accepted Answer

$1.69$

Vedclass · Answer

The data is obtained in tabular form as follows.


	
		
			${x_i}$
			${f_i}$
			${f_i} = \frac{{{x_i} - 64}}{1}$
			${y_i}^2$
			${f_i}{y_i}$
			${f_i}{y_i}^2$
		
		
			$60$
			$2$
			$-4$
			$16$
			$-8$
			$32$
		
		
			$61$
			$1$
			$-3$
			$9$
			$-3$
			$9$
		
		
			$62$
			$12$
			$-2$
			$4$
			$-24$
			$48$
		
		
			$63$
			$29$
			$-1$
			$1$
			$-29$
			$29$
		
		
			$64$
			$25$
			$0$
			$0$
			$0$
			$0$
		
		
			$65$
			$12$
			$1$
			$1$
			$12$
			$12$
		
		
			$66$
			$10$
			$2$
			$4$
			$20$
			$40$
		
		
			$67$
			$4$
			$3$
			$9$
			$12$
			$36$
		
		
			$68$
			$5$
			$4$
			$16$
			$20$
			$80$
		
		
			 
			$100$
			$220$
			 
			$0$
			$286$
		
	


Mean, $\bar x = A\frac{{\sum\limits_{i = 1}^9 {{f_i}{y_i}} }}{N} 	imes h = 64 + \frac{0}{{100}} 	imes 1 = 64 + 0 = 64$

Variance,   ${\sigma ^2} = \frac{{{h^2}}}{{{N^2}}}\left[ {N\sum\limits_{i = 1}^9 {{f_i}{y_i}^2 - \left( {\sum\limits_{i = 1}^9 {{f_i}{y_i}^2} } ight)} } ight]$

$=\frac{1}{100^{2}}[100 	imes 286-0]$

$=2.86$

$	herefore$ Standard deviation $(\sigma)=\sqrt{2.86}=1.69$

ટૂંકી રીતનો ઉપયોગ કરીને મધ્યક અને પ્રમાણિત વિચલન શોધો.

${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$

${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

Similar Questions

મધ્યસ્થ વડે $40, 62, 54, 90, 68, 76 $ અવલોકનોના સરેરાશ વિચલનનો ચલનાંક કેટલો થાય ?

નીચે આપેલ માહિતી માટે વિચરણ અને પ્રમાણિત વિચલન શોધો :

${x_i}$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

${f_i}$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

વિચલ $x$ અને $u $ એ $u\,\, = \,\,\frac{{x\,\, - \,\,a}}{h}$વડે સંબંધીત હોય તો $\sigma_x$ અને $\sigma_u$ વચ્ચેનો સાચો સંબંધ $= …….$

$2, 4, 6, 8, 10$ નું વિચરણ શોધો.

${x_i}$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
${f_i}$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

${x_i}$	${f_i}$	${f_i} = \frac{{{x_i} - 64}}{1}$	${y_i}^2$	${f_i}{y_i}$	${f_i}{y_i}^2$
$60$	$2$	$-4$	$16$	$-8$	$32$
$61$	$1$	$-3$	$9$	$-3$	$9$
$62$	$12$	$-2$	$4$	$-24$	$48$
$63$	$29$	$-1$	$1$	$-29$	$29$
$64$	$25$	$0$	$0$	$0$	$0$
$65$	$12$	$1$	$1$	$12$	$12$
$66$	$10$	$2$	$4$	$20$	$40$
$67$	$4$	$3$	$9$	$12$	$36$
$68$	$5$	$4$	$16$	$20$	$80$
	$100$	$220$		$0$	$286$

${x_i}$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
${f_i}$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

ટૂંકી રીતનો ઉપયોગ કરીને મધ્યક અને પ્રમાણિત વિચલન શોધો. ${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$ ${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$