Comprehensive Calculator Guide
This calculator finds the correct average of several percentages, weighting each by its group size, and compares it with the simple average. If 80% of a class of 50 pass and 60% of a class of 150, the pass rate for all students is 65%, not 70%, because the bigger class counts for more. Useful for school results, branches, surveys and performance reports.
Why not just average the percentages
Averaging 80% and 60% treats a group of 50 as if it were as big as a group of 150. Instead, count each group’s successes (percentage × size), add them and divide by the total size: (40 + 90) ÷ 200 = 65%.
With equal group sizes both averages match. The simple average also fits when you want the average group rather than the average person.
How to Use
- Enter each percentage and its group size, at least two.
- Add up to three more groups if needed; leave unused ones empty.
- Press “Calculate the average” to see the weighted and simple averages.
Formula Used
Weighted average = Σ(percentage × size) ÷ Σ sizes | Simple = sum of percentages ÷ count
Practical Examples
- Example 1
- 80% of 50 and 60% of 150: weighted 65%, simple 70%.
- Example 2
- 92% of 400, 85% of 250, 70% of 100: weighted 86.73%, simple 82.33%.
Important Tips
- Say in reports which average you used.
Common Mistakes to Avoid
- Averaging percentages from groups of different sizes.
Frequently Asked Questions
- How do I average percentages?
- Multiply each by its group size, add, and divide by the total size.
- When is the simple average right?
- With equal group sizes, or when you want the average group.
- What is the average of 80% of 50 and 60% of 150?
- 65%, not 70%.