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(D) Given: $n_{1}=10, n_{2}=10$Means: $m_{1}=60, m_{2}=40$Standard deviations: $\sigma_{1}=4, \sigma_{2}=6$The formula for the combined standard devia

Vedclass · Accepted Answer

$11.2$

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(D) Given: $n_{1}=10, n_{2}=10$Means: $m_{1}=60, m_{2}=40$Standard deviations: $\sigma_{1}=4, \sigma_{2}=6$The formula for the combined standard deviation $\sigma$ is:$\sigma=\sqrt{\frac{n_{1} \sigma_{1}^{2}+n_{2} \sigma_{2}^{2}}{n_{1}+n_{2}}+\frac{n_{1} n_{2}(m_{1}-m_{2})^{2}}{(n_{1}+n_{2})^{2}}}$Substituting the values:$\sigma=\sqrt{\frac{10 	imes 4^{2}+10 	imes 6^{2}}{10+10}+\frac{10 	imes 10(60-40)^{2}}{(10+10)^{2}}}$$\sigma=\sqrt{\frac{160+360}{20}+\frac{100(20)^{2}}{400}}$$\sigma=\sqrt{\frac{520}{20}+\frac{100 	imes 400}{400}}$$\sigma=\sqrt{26+100}=\sqrt{126} \approx 11.22$

Size $(x_i)$	$3.5$	$4.5$	$5.5$	$6.5$	$7.5$	$8.5$	$9.5$
Frequency $(f_i)$	$3$	$7$	$22$	$60$	$85$	$32$	$8$

The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

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