नीचे दी गई प्रेक्षणों के दो समूहों की सांख्यि | vedclass

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Question

$\sigma^{2}=\frac{ n _{1} \sigma_{1}^{2}+ n _{2} \sigma_{2}^{2}}{ n _{1}+ n _{2}}+\frac{ n _{1} n _{2}}{\left( n _{1}+ n _{2}\right)}\left(\overline{

Vedclass · Accepted Answer

$5$

Vedclass · Answer

$\sigma^{2}=\frac{ n _{1} \sigma_{1}^{2}+ n _{2} \sigma_{2}^{2}}{ n _{1}+ n _{2}}+\frac{ n _{1} n _{2}}{\left( n _{1}+ n _{2}ight)}\left(\overline{ x }_{1}-\overline{ x }_{2}ight)^{2}$

$n _{1}=10, n _{2}= n , \sigma_{1}^{2}=2, \sigma_{2}^{2}=1$

$\overline{ x }_{1}=2, \overline{ x }_{2}=3, \sigma^{2}=\frac{17}{9}$

$\frac{17}{9}=\frac{10 	imes 2+ n }{ n +10}+\frac{10 n }{( n +10)^{2}}(3-2)^{2}$

$\frac{17}{9}=\frac{(n+20)(n+10)+10 n}{(n+10)^{2}}$

$17 n^{2}+1700+340 n=90 n+9\left(n^{2}+30 n+200ight)$

$8 n^{2}-20 n-100=0$

$2 n^{2}-5 n-25=0$

$(2 n+5)(n-5)=0 \Rightarrow n=\frac{-5}{2} \,(Rejected) , 5$

Hence $n =5$

	आकार	माध्य	प्रसरण
प्रेक्षण $I$	$10$	$2$	$2$
प्रेक्षण $II$	$n$	$3$	$1$

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$K^{2}-1$	$K^{2}-1$	$K^{2}-1$	$k-3$

ऊँचाई (सेमी में)	$70-75$	$75-80$	$80-85$	$85-90$	$90-95$	$95-100$	$100-105$	$105-110$	$110-115$
बच्चों की संख्या	$3$	$4$	$7$	$7$	$15$	$9$	$6$	$6$	$3$

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