# Average Percentage Calculator

Now you can easily average the percentages using this simple average percentage calculator. Moreover, you will also learn how to average percentages manually and the formulas used to do so.

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The process of averaging percentages is very similar to finding the mean of data samples. However, this is only possible if the percentage sample sizes are similar. For different sample sizes, we must use a specific formula to average the percentages.

Throughout this article, we will explain how to calculate the percentage average for both the same and different sample sizes step-by-step.

## How to Use Average Percentage Calculator?

• It is quite easy to use this calculator to determine the average of percentages.
• The initial step is to choose an option from the drop-down menu. Select ‘yes’ if the sample sizes are the same, and ‘no’ if they are different.
• Choose how many entries you wish to average. We are currently only able to accept eight entries.
• Enter the percentage number and the sample size based on your choice to determine the average percentage value.

## Formula To Average Percentage

For calculating the average of percentages, use the formulas below. Use the first formula if the sample size are the same, and the second formula if they differ.

## How to Average Percentages?

Similar to performing an arithmetic average, averaging percentages is only achievable when all sample sizes are equal. However, you might not apply the same arithmetic average formula if you have a different sample size for each percentage. Here, a separate formula must be used.

We will walk you through the process of solving issues in both types of conditions. Below are thorough examples of both scenarios that have been solved.

Example

1. A high school conducted its regular exams. The exam’s results were available. Of the nearly 60 students who took the test, 20 had scores of 65%, 20 of 75%, and the remaining 20 received scores of 85%. What is the class’s average grade?

Solution :

We can clearly see from the example that this is a case of the same sample size. As a result, we can apply the first formula mentioned above.

Students scored 65% = 20
Students scored 75% = 20
Students scored 85% = 20

We may omit the sample size value because it is clear that all of the percentages have comparable sample sizes. Simply ignore the value and use the first formula if the sample size of percentages is similar.

Using the average percentage formula (first),

Average Percentage = ( a1 + a2 + a3 ) / n
Average Percentage = (65+75+85) / 3
Average Percentage = 225 / 3
Average Percentage = 75%

The average percentage of the entire class is 75%

Example

2. Preliminary exams were held at a college of engineering. The exam results were made public. Of the roughly 85 students who took the test, 20 obtained scores of 53%, 18 received scores of 68%, 22 received scores of 71%, 19 students scored 75%, and the remaining 6 received scores of 80%. What is the average percentage of the college?

Solution :

We can clearly see from the example that this is a case of the different sample size. Each percentage has different sample size. As a result, we can apply the second formula mentioned above.

Students scored 53% = 20
Students scored 68% = 18
Students scored 71% = 22
Students scored 75% = 19
Students scored 80% = 6

Using the average percentage formula (second),

Average Percentage = ( a1*w1 + a2*w2 + a3*w3 + a4*w4 + a5*w5 ) / ( w1+w2+w3+w4+w5 )
Average Percentage = [(53*20)+(68*18)+(71*22)+(75*19)+(80*6)] / (20+18+22+19+6)
Average Percentage = [(1060)+(1224)+(1562)+(1425)+(480)] / (85)
Average Percentage = 5751/85
Average Percentage = 67.6%

The average percentage of the college is 67.6%