ધારોકે વર્ગ Aના 100 વિદ્યાર્થીઓના ગુણનો | vedclass

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Question

$A$
			$B$
			$A+B$
		
		
			$\overline{ x }_1=40$
			$\overline{ x }_2=55$
			$\overline{ x }=50$
		
		
			$\sigma_1=\alpha$

Vedclass · Accepted Answer

$500$

Vedclass · Answer

$A$
			$B$
			$A+B$
		
		
			$\overline{ x }_1=40$
			$\overline{ x }_2=55$
			$\overline{ x }=50$
		
		
			$\sigma_1=\alpha$
			$\sigma_2=30-\alpha$
			$\sigma^2=350$
		
		
			$n _1=100$
			$n _2= n$
			$100+ n$
		
	


$\overline{ x }=\frac{100 	imes 40+55 n }{100+ n }$

$5000+50 n =4000+55 n$

$1000=5 n$

$n =200$

$\sigma_1{ }^2=\frac{\sum x _{ i }^2}{100}-40^2$

$\sigma_2{ }^2=\frac{\sum x _{ j }^2}{100}-55^2$

$350=\sigma^2=\frac{\sum x _{ i }^2+\sum x _{ j }^2}{300}-(\overline{ x })^2$

$350=\frac{\left(1600+\alpha^2ight) 	imes 100+\left[(30-\alpha)^2+3025ight] 	imes 200}{300}-(50)^2$

$2850 	imes 3=\alpha^2+2(30-\alpha)^2+1600+6050$

$8550=\alpha^2+2(30-\alpha)^2+7650$

$\alpha^2+2(30-\alpha)^2=900$

$\alpha^2-40 \alpha+300=0$

$\alpha=10,30$

$\sigma_1^2+\sigma_2^2=10^2+20^2=500$

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