Check out some similar questions!

agate5152 · Nov 7, 2011, 07:42 AM

Q.3. The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. Find the mean and standard deviation of the sample of size 150 obtained by combining the two samples

Unknown008 · Nov 7, 2011, 08:59 AM

If you don't know how to do it, break it down in terms you know.

$\bar{x} = \frac{\Sigma x}{50} = 54.1$

$\Sigma x = 54.1(50)$

$\bar{y} = \frac{\Sigma y}{100} = 50.3$

$\Sigma x = 50.3(100)$

$\sigma(x) = \sqrt{\frac{\Sigma^2 x}{50} - $\frac{\Sigma x}{50}$^2} = 8$

$\frac{\Sigma^2 x}{50} - (54.1)^2 = 8^2$

$\Sigma^2 x = 50(8^2 + (54.1)^2)$

$\sigma(y) = \sqrt{\frac{\Sigma^2 y}{100} - $\frac{\Sigma y}{100}$^2} = 7$

$\frac{\Sigma^2 y}{100} - (50.3)^2 = 7^2$

$\Sigma^2 y = 100(7^2 + (50.3)^2)$

From there, you can add both, since both are sums, and then use the mean and standard deviation formulae to get the required.