To calculate the weighted average mean, you need to follow a specific process that takes into account the importance, or weight, of each value in your dataset.
Steps to Calculate Weighted Average
Here's a clear breakdown of how to find the weighted average mean:
- Multiply Values by Weights: Begin by multiplying each value in your dataset by its corresponding weight. These weights reflect how much each value contributes to the overall average.
- Sum the Products: Next, add up all the products you calculated in step one. This gives you the total weighted value.
- Sum the Weights: Separately, sum all the individual weights. This gives you the total weight.
- Divide: Finally, divide the total weighted value (from step 2) by the sum of the weights (from step 3). The result is your weighted average mean.
Example
Let's illustrate this with an example:
| Value | Weight | Value x Weight |
|---|---|---|
| 10 | 2 | 20 |
| 20 | 3 | 60 |
| 30 | 5 | 150 |
| Totals | 10 | 230 |
Weighted Average Mean = (20 + 60 + 150) / (2 + 3 + 5) = 230 / 10 = 23
Important Points
- Percentages: When weights are percentages, their sum often equals 1 or 100%.
- Practical Use: Weighted averages are used in various fields, including academics (grading), finance (portfolio returns), and statistics, where certain values are more important than others.
In summary, calculating a weighted average involves multiplying each value by its weight, summing these products, and then dividing by the total sum of weights. This results in a mean that accounts for the relative importance of each individual value.
