# Weighted Average

StatisticsVariableAverageExpected Value → Weighted Average

Some points are more important than others. And, some results contribute more than others to the final result. Weighted average is an average where different quantities have different weight. And, it is calculated using the formula

$\textrm{Weighted Average}=w_1x_1+w_2x_2+w_3x_3+...+w_nx_n$

or

$\textrm{Weighted Average}=\sum_{i=1}^{n}w_ix_i$

Example 1. In a particular module an assignment contributes 30%, and final exam 70% to the final result. A student obtained 80% marks in assignment and 65% in the final exam. What are average marks?

$\textrm{Weighted Average}=0.3\times 80+0.7\times 65 \\ = 69.5$

So, the student obtained 69.5% marks in the module.

Portfolio Return
An investor usually invests in different assets. And, the combination of the assets hold by an investor is called portfolio.

Consider the portfolio that consists of two assets. The percentage investment (weight) and return on each investment is given the following table.

 Asset Investment Return A 40% 7% B 60% 5%

Example 2. Return on each investment is given in the above table. What is the portfolio Return?

Solution
The portfolio return is the weighted average of the assets’ returns.

$\textrm{Weighted Average}=0.4\times 7+0.6\times 5 \\ = 5.8$

Hence, the portfolio return is 5.8%.

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