Question

A candidate obtains 46 marks in English , 67 in Mathematics , 53 in Hindi , 72 in History and 58 in Economics. It is agreed to give triple weights to marks in English and Double weights to marks in Mathematics as compared to other subjects . Calculate Weighted Mean. Also, compare it with simple Arithmetic Mean.

Answer 1

Subject	Mark (%) (X)	Weight (W)	WX
English Mathematics Hindi History Economics	46 67 53 72 58	3 2 1 1 1	138 134 53 72 58
	ΣX = 296	ΣW = 8	ΣWX = 455

The given information can be summarised as above.

$$\begin{gathered} \mathrm{Simple}\mathrm{Arithmetic}\mathrm{Mean} \\ \overline{X}=\frac{\Sigma X}{N}=\frac{296}{5}=59.2 \\ \mathrm{Weighted}\mathrm{Arithmetic}\mathrm{Mean} \\ {\overline{\mathit{X}}}_{\mathit{w}}=\frac{\Sigma WX}{\Sigma W}=\frac{455}{8}=56.9 \end{gathered}$$
Thus, the weighted arithmetic mean is greater than the simple arithmetic mean.