Discussion

Find the weighted mean for the following data :

Value :	10	12	15	18	20
Weight :	2	5	12	4	7

Answer: C

The weighted mean is about 15.7.

Multiply each value by its weight, add, and divide by the total weight:

\[ \begin{aligned} \textstyle\sum wx &= 20 + 60 + 180 + 72 + 140 = 472 \\ \textstyle\sum w &= 2 + 5 + 12 + 4 + 7 = 30 \end{aligned} \]

\[ \bar{x}_{w} = 472/30 = 15.73 \]

The simple mean of the five values is \(75/5 = 15\), which ignores the weights. 15.2, 15.6 and 14.3 come from arithmetic slips.

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