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

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$\sqrt{96}$

$\sqrt{106}$

$\sqrt{126}$

answer is D.

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Detailed Solution

$n_{1} = 10, n_{2} = 10$
Average $m_{1} = 60 m_{2} = 40$
$σ_{1} = 4; σ_{2} = to$
$Standard deviation of Combined series σ = \sqrt{\frac{n_{1} σ_{1}^{2} + n_{2} σ_{2}^{2}}{n_{1} + n_{2}} + \frac{m_{1} n_{2} {(m_{1} - m_{2})}^{2}}{{(n_{1} + n_{2})}^{2}}}$ $= \sqrt{126}$

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