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

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.