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Question

$\mathrm{n}_{1}=10, \mathrm{n}_{2}=10$

average $\mathrm{m}_{1}=60, \mathrm{m}_{2}=40$

$\sigma_{1}=4, \sigma_{2}=6$

Standard deviation of comb

Vedclass · Accepted Answer

$11.2$

Vedclass · Answer

$\mathrm{n}_{1}=10, \mathrm{n}_{2}=10$

average $\mathrm{m}_{1}=60, \mathrm{m}_{2}=40$

$\sigma_{1}=4, \sigma_{2}=6$

Standard deviation of combined series

$\sigma=\sqrt{\frac{n_{1} \sigma_{1}^{2}+n_{2} \sigma_{2}^{2}}{n_{1}+n_{2}}+\frac{n_{1} n_{2}\left(m_{1}-m_{2}ight)^{2}}{\left(n_{1}+n_{2}ight)^{2}}}$

$=\sqrt{\frac{10 	imes 16+10 	imes 36}{10+10}+\frac{10 	imes 10(60-40)^{2}}{(10+10)^{2}}}$

$=\sqrt{8+18+100}=\sqrt{126}=11.2$

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

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