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Calculate the average of multiple percentages using simple or weighted averaging. Understand when each method is appropriate.
Enter at least 2 percentages to calculate average
Example: Average of 10%, 20%, 30% = (10 + 20 + 30) / 3 = 20%
Example: 80% (weight 3) and 60% (weight 1) = (80×3 + 60×1) / (3+1) = 300/4 = 75%
Example: Two classes' test scores:
Simple average: (80% + 60%) / 2 = 70%
Weighted average: (80×5 + 60×20) / (5+20) = 64%
The weighted average is correct because it accounts for the different class sizes!
| Percentages | Simple Average | Weighted (1:2 ratio) |
|---|---|---|
| 20%, 30% | 25% | 26.67% |
| 50%, 70% | 60% | 63.33% |
| 10%, 90% | 50% | 63.33% |
| 75%, 85% | 80% | 81.67% |
| 40%, 60% | 50% | 53.33% |
For simple average: add all percentages and divide by the count. For weighted average: multiply each percentage by its weight, sum those products, and divide by the sum of weights. Use weighted when the percentages apply to different-sized groups.
Use weighted average when the percentages apply to groups of different sizes. For example, averaging test scores from classes of different sizes, combining sales data from regions of different populations, or averaging rates from different time periods of varying lengths.
You can, but it's often wrong! Simply averaging percentages assumes each percentage has equal weight, which is rarely true in real situations. For example, averaging 10% growth in one product and 50% in another ignores their different sales volumes.
The main issue is that percentages are relative - they depend on what they're percentages OF. A 50% increase on $100 is different from 50% on $1000. Simple averaging treats them equally when they shouldn't be. This is why weighted averaging based on the underlying values is more accurate.
Add the two percentages and divide by 2. For example, the average of 25% and 35% is (25+35)/2 = 30%. However, this is only correct if both percentages apply to equal-sized bases. Otherwise, use weighted average.
Mean and average are the same thing - both refer to the sum divided by count. When applied to percentages, you get an "average percentage." The key distinction is between simple (unweighted) and weighted averages, not between mean and average.
Be careful! You can't simply average percentage increases. If sales increased 10% then 20%, the total isn't 15% - it's 1.10 × 1.20 = 1.32 = 32% total. To find the average annual rate: take the geometric mean: √(1.10 × 1.20) - 1 ≈ 14.9%.
With simple average, no - it must be between the minimum and maximum. But with negative weights (which are unusual), mathematically it's possible. In normal use cases with positive weights, the weighted average will always fall between the minimum and maximum percentages.