Everybody knows how to calculate the percentage of any amount or number. However, did you know that there is a formula for calculating the average of a percentage, otherwise known as the average percentage formula?
In this article, we will talk about how percentages work, how to calculate percentages and how to calculate average percentages using an example.
How Are Percentages Calculated?
In simple terms of O Level & IGCSE Mathematics, percentages are portions of something out of 100.
Example:
For example, if you had a box containing 100 candies out of which 60 were orange flavoured, then that would mean 60% of the total candies are orange flavoured.
Calculating percentages helps because it puts into perspective how much of a certain amount is either being used or considered. In the real world, we are surrounded by percentages that represent different things such as taxes, results of a survey, etc. Percentages help attach meaning to these figures.
How to Calculate Average Percentage?
Before we delve into how to calculate the average percentage formula, we must explore how to calculate the average. The average of a set of numbers is basically:
The sum of all numbers/The total number of values in a set
So, for example, if you have certain numbers in a set i.e. 21, 35, 87, 49, 17, then just add all the numbers (21+35+87+49+17 = 209) and divide the answer by the total number of values in the set (in this case, 5).
209/5 = 41.8
Additional Steps You May Consider:
When calculating the average percentage, there are several additional steps you may have to consider:
Step 1: Convert percentages into decimals
Let’s say you have two percentages of certain sample sizes or totals that you need to calculate the average percentage for; 67% of 150 and 23% of 350. The first step will be to convert these percentages into decimals. You can do this by dividing both percentages by 100.
67% = 67/100 = 0.67
23% = 23/100 = 0.23
Step 2: Determine the number that each decimal represents
Once you have converted percentages into decimals, you will have to figure out what each decimal represents from the total. For this, you will have to multiply the decimals by each sample total.
0.67 × 150 = 100.5 ~ 101
0.23 × 350 = 80.5 ~ 81
(For the above example, both answers have been rounded off to the nearest decimal)
Step 3: Add both numbers and sample size totals
Now that you have the numbers for each decimal, it is time to add both numbers along with their sample size totals.
101 + 81 = 182
150 + 350 = 500
Step 4: Calculate the percentage average
To get the average percentage, you will have to divide the sum of the two percentages by the sum of the two sample size totals.
182/500 = 0.364
Then, to convert the decimal into a percentage, you will multiply the answer by 100.
0.364 × 100 = 36.4%
So, the average percentage formula can be described as follows:
(Percentage 1 + Percentage 2) / (Sample size total 1 + Sample size total 2) × 100
Calculating the Average Percentage Using a Real-Life Example
ABC University wants to determine the average percentage of students who have graduated from two separate batches in the same year. In the first batch, there were a total of 1500 students out of which 55% graduated whereas in the second batch, there were a total of 1200 students out of which 48% graduated.
Working:
55/100 = 0.55
48/100 = 0.48
0.55 × 1500 = 825
0.48 × 1200 = 576
825 + 576 = 1401
1500 + 1200 = 2700
1401/2700 = 0.52
0.52 × 100 = 52%
Using this formula, the average percentage of students who have graduated from two batches in the same year comes to 52%.
Conclusion
Understanding how to calculate the average percentage formula adds another layer of depth to your mathematical toolkit. As we've navigated converting percentages to decimals, determining averages, and applying these concepts in real-life scenarios, it's evident that percentages aren't just numbers; they're windows into meaningful insights.
Whether you're a student crunching numbers for academia or someone deciphering data in the professional arena, the ability to calculate average percentages equips you with a valuable skill.
So, the next time you encounter sets of percentages beckoning for calculation, approach them with confidence, armed with the knowledge of the average percentage formula. Happy calculating!
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