Question

The mean income of a group of workers is $\overline{X}$ and that of another group is $\overline{Y}$. If the number of workers in the second group is $10$ times the number of workers in the first group, then the mean income of combined group is

Answer 1

Let no of workers in first group = n

then no of workers in second group = 10n

$\therefore \left(\frac{X_1+X_2+........+X_n}{n}\right)=\overline{X}$

$and\left(\frac{Y_1+Y_2+........+Y_{10n}}{10n}\right)=\overline{Y}$

$\therefore$combined group mean

$=\left(\frac{(X_1+X_2+.....+X_n)+(Y_1+Y_2+.....+Y_{10n})}{11n}\right)$

$=\left(\frac{n\overline{X}+10n\overline{Y}}{11n}\right)=\left(\frac{\overline{X}+10\overline{Y}}{11}\right)$