Mean of two samples of size 200 and 300 were found to be 25, 10 respectively their S.D. is 3 an

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13.Statistics

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The mean of two samples of size $200$ and $300$ were found to be $25, 10$ respectively their $S.D.$ is $3$ and $4$ respectively then variance of combined sample of size $500$ is :-

A

$64$

B

$65.2$

C

$67.2$

D

$64.2$

Solution

$\mathrm{x}_{1}=200 \quad \mathrm{x}_{2}=300$

$\overline{\mathrm{x}}_{1}=25 \quad \overline{\mathrm{x}}_{2}=10$

$\sigma_{1}=3 \quad \sigma_{2}=4$

combined mean $=\frac{25 \times 200+10 \times 300}{500}=16$

$\sigma_{1}^{2}=9=\frac{1}{200}\left(\sum x_{i}^{2}\right)-625$

$126800=\sum x_{i}^{2}$

$\sigma_{2}^{2}=16=\frac{1}{300} \sum y_{1}^{2}-100$

$34800=\sum y_{1}^{2}$

$\sigma^{2}=\frac{1}{500}(126800+34800)-(16)^{2}$

$=323.2-256=67.2$

Standard 11

Mathematics

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