How To Calculate Weighted average in Mathematics: Definition, Formula, and Examples

How To Calculate Weighted average

Definition: A weighted average is a statistical measure that gives more importance or weight to certain values in a data set.

Formula: The formula for a weighted average is as follows:

Weighted Average = (Sum of (value * weight)) / (Sum of weights)

Types of Weighted Average:

1. Simple Weighted Average: In this type of weighted average, the weights assigned to each value are equal.
2. Complex Weighted Average: In this type of weighted average, the weights assigned to each value are unequal.

Need for Weighted Average:

1. Importance of Data: Weighted average is used to emphasize the importance of certain values in a data set.
2. Priority: Weighted average can be used to give priority to certain values over others in a data set.

How to Use Weighted Average:

1. Determine the weights to be assigned to each value in the data set.
2. Calculate the sum of (value * weight) for each value in the data set.
3. Calculate the sum of weights.
4. Calculate the weighted average by dividing the sum of (value * weight) by the sum of weights.

Example: Consider a data set with values [10, 20, 30, 40] and corresponding weights [1, 2, 3, 4]. The weighted average can be calculated as follows:

Weighted Average = (10 * 1 + 20 * 2 + 30 * 3 + 40 * 4) / (1 + 2 + 3 + 4) = (10 + 40 + 90 + 160) / 10 = 300 / 10 = 30

Note: The weighted average is a useful statistical measure that takes into account the importance of different values in a data set.