Introduction
In business mathematics and statistics, averages are used to find central values or representative figures from data. However, not all data points carry the same level of importance. That’s where the concept of a weighted average comes in. In this answer, we will explain what a weighted average is and when it is preferable over a simple average.
What is a Weighted Average?
A weighted average is a type of average where each value in the dataset is multiplied by a weight, which represents its relative importance. After multiplying, the results are summed and then divided by the total sum of the weights.
Formula:
Weighted Average = (w₁x₁ + w₂x₂ + w₃x₃ + … + wₙxₙ) / (w₁ + w₂ + w₃ + … + wₙ)
Where:
- x₁, x₂, …, xₙ are the values
- w₁, w₂, …, wₙ are the corresponding weights
Example of Weighted Average
Suppose a student has the following marks in three subjects:
- Maths: 80 (weight 4)
- English: 70 (weight 3)
- Science: 90 (weight 2)
Weighted Average = (80×4 + 70×3 + 90×2) / (4+3+2) = (320 + 210 + 180) / 9 = 710 / 9 ≈ 78.89
If we had used a simple average, it would be (80 + 70 + 90)/3 = 80. This shows that weighted average gives a different and more accurate result when subjects or components are not equally important.
What is a Simple Average?
A simple average or arithmetic mean is calculated by adding all the values and dividing by the number of values.
Simple Average = (x₁ + x₂ + x₃ + … + xₙ) / n
It assumes that all values are equally important or have equal weight.
Conditions When Weighted Average is Preferable
A weighted average is preferred over a simple average in the following conditions:
1. When Items Have Different Importance
If some items contribute more than others, then using weights ensures that the average reflects true significance.
Example: In calculating grade point averages where different subjects carry different credit hours.
2. In Financial Calculations
Stock analysts use weighted averages to find average returns when different stocks are held in different amounts.
Example: Weighted average cost of capital (WACC) is used in corporate finance.
3. In Statistics and Data Analysis
In surveys, if data is collected from different groups of different sizes, weighted averages provide accurate representation.
Example: In population studies or market research where one group may be overrepresented.
4. In Production and Inventory Management
To calculate the cost of goods sold or inventory valuation when items have different costs or quantities.
Example: Weighted average method is used in inventory costing.
5. In Voting Systems
In some elections or corporate decisions, votes may carry different weights based on stake or position. A weighted average reflects this better.
Conclusion
A weighted average is a more realistic and practical way of calculating an average when different data points have different significance. It gives more accurate results in scenarios where the contribution of each value is not equal. In contrast, a simple average works well only when all values are equally important. Thus, in business, education, finance, and statistics, knowing when to apply a weighted average helps in making better decisions based on data.