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Weighted Average
Weighted Average
The weighted average is a calculation method that finds the average of a set of numbers, where each number is assigned a weight. The weights are used to account for the relative importance of each number in the calculation.
Formula for Weighted Average:
Weighted Average = (Sum of Weighted Values) / Total Weight
Where:
- Weighted Average is the average of the weighted numbers.
- Sum of Weighted Values is the sum of the products of each number and its weight.
- Total Weight is the total of the weights assigned to each number.
Process:
- Assign weights to each number.
- Multiply each number by its weight.
- Sum the weighted values.
- Divide the sum of weighted values by the total weight.
Example:
A student has the following grades:
- 80% with a weight of 0.5
- 90% with a weight of 0.3
- 70% with a weight of 0.2
Weighted Average = (80% * 0.5 + 90% * 0.3 + 70% * 0.2) / (0.5 + 0.3 + 0.2) = 84%
Applications:
- Calculating averages when weights are assigned to different items or elements.
- Weighted averages are commonly used in statistics, finance, and engineering.
- They are used to account for factors such as importance, frequency, or probability.
Advantages:
- Allows for the incorporation of different weights.
- Provides a more accurate representation of average when weights are used.
- Can be used to calculate averages for complex datasets.
Disadvantages:
- Can be complex to calculate, especially for large datasets.
- Requires careful selection of weights.
- Can be biased if weights are not chosen appropriately.
