When used for analytical purposes, calculating a simple average can be misleading. By applying weights to certain numbers in a list, you can achieve a much more precise understanding.
Not all information has the same level of importance, and any insightful analysis of a sector needs to account for this factor. Relying on straightforward formulas like the average of a number series often leads to inadequate decisions.
Let’s consider a straightforward example to illustrate this. At the end of the year, a teacher uses the following criterion to determine if students can advance to the next grade: their average score must be higher than 10. Here is a simplified table with the scores of several students.
| Joey | Monica | Rachel | |
|---|---|---|---|
| Test 1 | 12 | 7 | 11 |
| Midterm Exam | 9 | 12 | 12 |
| Test 2 | 14 | 6 | 10 |
| End-of-Year Exam | 8 | 14 | 11 |
| Average | 10,75 | 9,75 | 11 |
Here, we have three students: Joey, Monica, and Rachel. Each has been assessed through four different exams: Test 1, the Midterm Exam, Test 2, and so on.
By applying an average to these scores, it appears that two students have a sufficient score to advance: Joey and Rachel. Monica, on the other hand, does not pass.
What is the Principle of Weighted Average?
When calculating a weighted average, we consider that not all exams have the same significance. For instance, the Midterm Exam is twice as important as the tests. Similarly, the End-of-Year Exam is four times as important as a single test since it encompasses all concepts taught throughout the year.
The weighted average takes this into account by assigning a weight to each exam. Therefore, tests have a coefficient of 1, the Midterm Exam a coefficient of 2, and the End-of-Year Exam a coefficient of 4.
From there, the weighted average is calculated as follows:
(score x coefficient) + (score x coefficient) + (…) / sum of coefficients
| coefficient | Joey | Monica | Rachel | |
|---|---|---|---|---|
| Test 1 | 1 | 12 | 7 | 11 |
| Midterm Exam | 2 | 18 | 24 | 24 |
| Test 2 | 1 | 14 | 6 | 10 |
| End-of-Year Exam | 4 | 32 | 56 | 44 |
| Weighted Average | 9,5 | 11,63 | 11,13 |
For example, Joey’s weighted average is calculated as follows: (12 x 1) + (9 x 2) + (14 x 1) + (8 x 4) / 8. And what does this calculation reveal? A completely different scenario. Now, Monica emerges as the top student and passes with flying colors, while Joey does not!
What are the Advantages of the Weighted Average?
As this example demonstrates, the weighted average provides a much clearer picture of each student’s level. This creates a tool that enables informed decision-making.
Consider an online store collecting customer reviews. It has a trigger system: if average ratings fall below 3 out of 5 over a week, corrective actions must be promptly taken. But imagine that among its customers, there are 5 key clients representing 60% of the revenue. Their opinions are crucial, so their ratings should carry more weight than those of occasional buyers. As such, the weighted average can highlight underlying trends that might go unnoticed.
How to Weigh a Portfolio of Stocks?
The concept of the weighted average is so crucial that it is utilized when calculating the capital gains an investor must report to tax authorities following stock sales. Once again, an example clarifies the necessity of this calculation.
Consider an investor who buys:
- 100 shares at €20 from a startup in the first year
- 200 shares at €50 from the same startup the next year.
If the investor merely uses a “simple” average based on what was spent, they get an average of €35. However, this is misleading because it gives equal importance to the amounts paid (€20 and €50). Selling shares for €38 might falsely appear as a profit. In reality, it isn’t.
To find the weighted average, multiply the 100 shares by €20 for the first year and the 200 shares by €50 for the second year: 2,000 + 10,000 equals 12,000 euros in total. This sum is then divided by the total number of shares acquired (300). You get a weighted average of €40, suggesting that a sale at €38 would actually mean a loss.
How is it a Tool for Decision Making?
The weighted average helps determine whether it’s wise to act on a particular situation. Thus, it serves as an essential analytical tool not to be missed.
