Question

Calculate weighted mean of the following data by using Direct and Short-cut Methods:

Items	81	76	74	58	70	73
Weight	2	3	6	7	3	7

Answer 1

Items (X)	Weight (W)	WX	Deviation d = X − A	Wd
81 76 74 = A 58 70 73	2 3 6 7 3 7	162 228 444 406 210 511	7 2 0 −16 −4 −1	14 6 0 −112 −12 −7
	∑W = 28	∑WX = 1961		∑Wd = −111

Direct Method
$$\begin{gathered} {\overline{X}}_w=\frac{\Sigma WX}{\Sigma W} \\ =\frac{1961}{28}=70.04 \end{gathered}$$

Shortcut Method
$$\begin{gathered} X_w=A+\frac{\Sigma Wd}{\Sigma W} \\ =74+\left(\frac{-111}{28}\right) \\ =74-3.964 \\ =\; 70.04 \end{gathered}$$
Hence, the weighted mean is 70.04