Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. Unlike a simple arithmetic average where all values are treated equally, weighted average assigns different weights to different values.
Definition of Weighted Average
A weighted average is calculated by multiplying each value by its corresponding weight, summing all these products, and then dividing by the sum of all weights. This method is particularly useful when some values should have more influence on the final result than others.
Weighted Average Formula
Weighted Average = Σ(value × weight) / Σ(weight)
Where Σ represents the sum of all products of values and their weights, divided by the sum of all weights.
How to Calculate Weighted Average
- 1. Multiply each value by its corresponding weight
- 2. Sum all the products from step 1
- 3. Sum all the weights
- 4. Divide the sum of products by the sum of weights
Example Calculation
Let's say you have three test scores: 80 (weight 1), 90 (weight 2), and 70 (weight 3). First, multiply each score by its weight: 80×1=80, 90×2=180, 70×3=210.
The weighted average is: (80 + 180 + 210) / (1 + 2 + 3) = 470 / 6 = 78.33
Common Uses of Weighted Average
Weighted averages are used in many real-world scenarios:
- Academic grading where different assignments have different weights
- Financial portfolio analysis where investments have different sizes
- Statistical analysis where data points have different reliabilities
- Quality control where measurements have different precisions