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:

1. Assign weights to each number.
2. Multiply each number by its weight.
3. Sum the weighted values.
4. 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.