Question

The average income of a group of persons is $\overline{x}$ and that of another group is $\overline{y}.$ If the number of persons of both group are in the ratio 4 : 3, then average income of combined group is

• A. $\frac{\overline{x}+\overline{y}}{7}$
• B. $\frac{3\overline{x}+4\overline{y}}{7}$
• C. $\frac{4\overline{x}+3\overline{y}}{7}$
• D. None of these

Answer 1

The correct option is C $\frac{4\overline{x}+3\overline{y}}{7}$

Here weight ratio is, $w_1:w_2=\frac{4}{3}$ (i)
Hence required average
income of the combined group is $=\frac{\sum w_i{x}_i}{\sum w_i}=\frac{\overline{X}{w}_1+\overline{Y}{w}_2}{w_1+w_2}=\frac{\overline{X}\frac{w_1}{w_2}+\overline{Y}}{1+\frac{w_1}{w_2}}=\frac{4\overline{X}+3\overline{Y}}{7}$
using (i)