Question

Daily wages of 50 workers of a factory are given below:-
Daily wages in Rs :- Workers
100 - 120 12
120 - 140 f
140 - 160 8
160 - 180 6
180 - 200 10
Find the missing frequency and hence find the mean daily wage of the workers.

Answer 1

$$\begin{gathered} \mathrm{Here}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{frequencies}\mathrm{is}, \\ \sum _{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}=36+\mathrm{f} \\ \mathrm{and}\mathrm{total}\mathrm{frequency}\mathrm{is}50. \\ \mathrm{This}\mathrm{gives} \\ 36+\mathrm{f}=50 \\ \mathrm{f}=50-36 \\ \mathrm{f}=14 \\ \mathrm{Consider}\mathrm{the}\mathrm{following}\mathrm{table}. \\ \mathrm{Daily}\mathrm{Wages}{\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}\text{'}\mathrm{s}{\mathrm{d}}_{\mathrm{i}}={\mathrm{x}}_{\mathrm{i}}-\mathrm{A}{\mathrm{u}}_{\mathrm{i}}=\frac{{\mathrm{d}}_{\mathrm{i}}}{20}{\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}} \\ 100-12012110-40-2-24 \\ 120-14014130-20-1-14 \\ 140-1608\mathrm{A}=150000 \\ 160-18061702016 \\ 180-200\underline{10}190402\underline{20} \\ \sum _{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}=50\sum _{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}=-12 \\ \mathrm{Thus}\mathrm{the}\mathrm{required}\mathrm{mean}\mathrm{daily}\mathrm{wage}\mathrm{of}\mathrm{the}\mathrm{workers}\mathrm{is}, \\ \overline{\mathrm{x}}=\mathrm{A}+\frac{\sum _{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}}{\sum _{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}}\times \mathrm{h} \\ =150+\frac{-12}{50}\times 20 \\ =150+\frac{-24}{5} \\ =150-4.8 \\ =\mathbf{145}\mathbf{.}\mathbf{2}\mathbf{}\mathbf{}\mathbf{}\mathbf{} \end{gathered}$$