When it comes to calculating percentages, most of us are quite familiar with the process. For example, calculating a 20% discount on a $100 item is easy – you simply multiply 100 by 0.2 to get $20 off, making the total cost $80. But what happens when you need to average two or more percentages together? Is it as simple as adding them up and dividing by the number of percentages? Let’s find out!
The Basics of Percentages
Before we dive into averaging percentages, let’s do a quick refresher on the basics of percentages. A percentage is simply a way of expressing a fraction as a part of 100. For example, if you eat 4 out of 10 cookies, you’ve eaten 40% of the cookies.
To convert a percentage to its decimal equivalent, you divide by 100. So, 40% becomes 0.4. To convert a decimal back to a percentage, you multiply by 100. So, 0.4 becomes 40%.
Adding Percentages
When it comes to adding percentages, the answer is – it depends. If the percentages are referring to the same base (i.e. the same total amount), you can simply add them together. For example, if you score 80% on one test and 90% on another test, your total score would be 170%.
However, if the percentages are referring to different bases (i.e. different total amounts), you need to use a weighted average. This means you calculate the average based on how much each percentage contributes to the total.
Weighted Averages
Weighted averages are used when you want to calculate an average that takes into account the different importance or relevance of certain factors. For example, if you’re calculating your GPA, your grade in a more difficult class should be weighted more heavily than your grade in an easier class.
To calculate a weighted average of percentages, you need to first determine the weight of each percentage. The weight is usually expressed as a fraction or a percentage. For example, if you want to calculate the weighted average of two percentages where one carries a weight of 60% and the other carries a weight of 40%, you would multiply the percentages by their respective weights:
| Percentage | Weight | Weighted Percentage |
|---|---|---|
| 80% | 0.6 | 48% |
| 90% | 0.4 | 36% |
| Total | 84% | |
In this example, the total weighted percentage would be 84%.
Calculating the Average of Percentages
Now that we know how to add percentages and calculate weighted averages, we can finally tackle the question of whether or not you can average percentages. The answer is yes – but only if you use a weighted average.
Let’s say you want to calculate the average of three percentages: 20%, 50% and 80%, with each percentage having equal importance. You could simply add them up and divide by three, but this would not give an accurate representation of the average. Instead, you would need to use a weighted average:
| Percentage | Weight | Weighted Percentage |
|---|---|---|
| 20% | 0.33 | 6.67% |
| 50% | 0.33 | 16.67% |
| 80% | 0.33 | 26.67% |
| Total | 50% | |
In this example, the weighted average of the three percentages is 50%.
Conclusion
So, can you average percentages? The answer is yes – but only if the percentages have equal importance or if you use a weighted average that takes into account their respective weights. Adding percentages is only possible if they refer to the same base.
FAQs
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Can you average grades that are expressed as percentages?
Yes, you can average grades that are expressed as percentages using the same process as above.
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Can you average percentages without using a weighted average?
Yes, you can add percentages together and divide by the number of percentages, but this method only works if the percentages refer to the same base or have equal importance.
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Can you average percentages that are negative?
Yes, you can average percentages that are negative using the same process as above. The negative sign is simply included in the percentage value.
References
- Math Is Fun. (2021). Percentages. https://www.mathsisfun.com/percentages.html
- Study.com. (2021). Weighted Average: Definition, Formula & Example. https://study.com/academy/lesson/weighted-average-definition-formula-example.html
- University of Delaware. (2021). Weighted Average. https://www.mathsci.udel.edu/~braun/class/mat468/notes/weightedaverage.html