Answer :
The formulas for the mean and standard deviation of a population are:
[tex]\mu=\frac{1}{n}\Sigma_i\ x_i\\\\\sigma=\sqrt{\frac{1}{n}\Sigma_i\ (x_i-\mu)^2}\\[/tex]
The formulas for the mean and standard deviation of the total combined population, of two populations n1 and n2 with means μ1, μ2 and standard deviations σ1 and σ2 are as follows:
[tex]\mu=\frac{\mu_1\ n_1 + \mu_2\ n_2}{n_1+n_2}=\frac{25*235+25*237.5}{50}=236.25\\\\\sigma=\sqrt{\frac{n_1\ \sigma_1^2+n_2\ \sigma_2^2}{n_1+n_2}}=\sqrt{\frac{25*3^2+25*4^2}{50}}=\sqrt{12.5}=3.53[/tex]
I hope that is easy enough to follow.
[tex]\mu=\frac{1}{n}\Sigma_i\ x_i\\\\\sigma=\sqrt{\frac{1}{n}\Sigma_i\ (x_i-\mu)^2}\\[/tex]
The formulas for the mean and standard deviation of the total combined population, of two populations n1 and n2 with means μ1, μ2 and standard deviations σ1 and σ2 are as follows:
[tex]\mu=\frac{\mu_1\ n_1 + \mu_2\ n_2}{n_1+n_2}=\frac{25*235+25*237.5}{50}=236.25\\\\\sigma=\sqrt{\frac{n_1\ \sigma_1^2+n_2\ \sigma_2^2}{n_1+n_2}}=\sqrt{\frac{25*3^2+25*4^2}{50}}=\sqrt{12.5}=3.53[/tex]
I hope that is easy enough to follow.