Question

The man height of 25 male workers in a factory is 61 inches and the mean height of 35 female workers in the same factory is 58 inches. Find the combined mean height of 60 workers in the factory

Answer 1

Combined Mean $\mathbf{(}\mathbf{}{\overline{\mathit{X}}}_{\mathit{m}\mathbf{,}\mathit{f}}\mathbf{)}$ = $\frac{N_m{\overline{X}}_m+N_f{\overline{X}}_f}{N_m+N_f}$
Here,

$$\begin{gathered} {\overline{X}}_m=61inches,{\overline{X}}_f=58inches \\ {N}_m=25,N_f=35 \end{gathered}$$

$$\begin{gathered} CombinedMean({\overline{X}}_{m,f})=\frac{25\times 61+35\times 58}{25+35} \\ or,{\overline{X}}_{m,f}=\frac{3555}{60} \\ \Rightarrow {\overline{X}}_{m,f}=59.25inches \end{gathered}$$

Hence, the combined mean height of the factory is 59.25 inches.