Question

A candidate obtains the following percentage of marks: Sanskrit 75, Mathematics 84, Economics 56, English 78, Politics 57, History 54, Geography 47,. It is agreed to give double weights to marks in English , Mathematics and Sanskrit . What is the weighted and simple arithmetic mean?

Answer 1

Subject	Marks (X)	Weight (W)	WX
Sanskrit Mathematics Economics English Politics History Geography	75 84 56 78 57 54 47	2 2 1 2 1 1 1	150 168 56 156 57 54 47
	ΣX = 451	ΣW = 10	ΣWX = 688

$$\begin{gathered} \overline{X}=\frac{\Sigma X}{N}=\frac{451}{7}=64.43\mathrm{Marks} \\ {\overline{X}}_{\mathrm{W}}=\frac{\Sigma WX}{\Sigma W}=\frac{688}{10}=68.8\mathrm{Marks} \end{gathered}$$
Thus, the weighted mean and simple arithmetic mean are 68.8 and 64.43 respectively.