The mean income of a group of individuals is | vedclass

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(A) Let the number of individuals in the two groups be $n_1$ and $n_2$ respectively.Given: $\bar{x}_1 = 400$,$\bar{x}_2 = 480$,and the combined mean $

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$5/3$

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(A) Let the number of individuals in the two groups be $n_1$ and $n_2$ respectively.Given: $\bar{x}_1 = 400$,$\bar{x}_2 = 480$,and the combined mean $\bar{x} = 430$.The formula for the combined mean is $\bar{x} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$.Substituting the values: $430 = \frac{400n_1 + 480n_2}{n_1 + n_2}$.$430(n_1 + n_2) = 400n_1 + 480n_2$.$430n_1 + 430n_2 = 400n_1 + 480n_2$.$430n_1 - 400n_1 = 480n_2 - 430n_2$.$30n_1 = 50n_2$.$\frac{n_1}{n_2} = \frac{50}{30} = \frac{5}{3}$.

The mean income of a group of individuals is $400$ and the mean income of another group of individuals is $480$. If the mean income of all the individuals in both groups combined is $430$,find the ratio of the number of individuals in the two groups.

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