Calculating the average percentage of a given set of data can be an intimidating task, but it doesn’t have to be. With a few simple steps, you can easily calculate the average percentage of any set of data. In this blog post, we’ll discuss the formula and how to calculate it, and provide some examples to help you understand it better. We’ll also discuss how to use the average percentage to compare sets of data and how it can be used in business and other settings. With this information, you’ll be able to easily compute the average percentage of any set of data and use it to make informed decisions.
To find the average percentage of the two percentages in this example, you need to first divide the sum of the two percentage numbers by the sum of the two sample sizes. So, 95 divided by 350 equals 0.27. You then multiply this decimal by 100 to get the average percentage.
Average percentages in Excel with a calculated field by Chris Menard
The weighted average of percentages
Remember the test results for five people from the example at the end of the section above? After learning how to find the average percentage, we got:
Equivalently, we could have written:
Clearly, the new notation is shorter. We can also see how many people received the same outcome right away: 444 received 80%80%80%, and 111 received 40%40%40%. To put it another way, rather than treating each entry individually, we group them together based on their score.
What we obtained is the weighted average of the percentages, with the weights reflecting the number of students who achieved the score. The calculations are fortunately the same as for the regular weighted average: if we have entries a1a_1a1, a2a_2a2, and a3a_3a3, , ana_nan with respective weights w1w_1w1, w2w_2w2, w3w_3w3, . , wnw_nwn, then:
If we translate the notation to our needs (i. e. , to explain how to average percentages), a1a_1a1, a2a_2a2, a3a_3a3, . subsequent percentages, while w1w_1w1, w2w_2w2, w3w_3w3, and ana_nan will not. wnw_nwn will be the corresponding sample sizes for the aforementioned percentages.
So what happens if all weights are the same (i. e. If we use www to represent the mutual weight, then: If all samples are the same size, then:
by the rules of fraction simplification. In other words, the weight is irrelevant, and the regular (non-weighted) average is equal to the weighted average of the percentages.
Overall, it is clear that understanding the standard weighted average is the key to understanding how to calculate the average percentage. However, let’s go through one more instance to demonstrate how it relates to actual statistics. We’ll also use the chance to do so to use Omni’s average percentage calculator.
Example of using the average percentage calculator
Let’s say we asked 1,000 people if they ate pancakes at least once a week. There were 250250250 people over the age of 50, 300300300 teenagers, and 450450450 adults. 64%64%64% of the first group claimed to consume pancakes on a weekly basis. It was 42%42%42% in the second and 36%36%36% in the third. Let’s figure out how to estimate the typical proportion of pancake eaters among our 1,000 people.
But first, let’s see how simple the task is with the help of the available average percentage calculator. There is a sample size question at the top of the tool. Since the groups in our situation vary in size, we decide against it.
This will cause more variable fields to appear below, corresponding to the percentages and sample sizes of the dataset. They appear in pairs, each dedicated to one group. Observe how there are initially only two of these sections visible, but as soon as you begin entering data, additional sections appear (the Omnis average percentage calculator allows for up to ten entries). Looking back at our example, we input subsequently:
The average percentage calculator will output the result below along with the intermediate steps once you enter the final value.
Now, lets see how to find the average percentage ourselves. First, we identify our dataset using the information from the aforementioned section: the following percentages are 64%64%64%, 42%42%42%, and 36%36%36%, with corresponding sample sizes of 300300300, 450450450, and 250250250 individuals. Next, we use the weighted average of percentages formula:
It turns out that, on average, 47. 1%47. 1%47. 1% of people eat pancakes every week. Perhaps we could add some new questions to the survey and conduct a more in-depth investigation, but do they have them once a week or every day?
To make calculations simpler, change each percentage to its decimal equivalent. Typically, it is simpler to enter the numbers into a calculator in decimal form. Divide each percentage by 100 to convert. For instance, to convert a percentage into decimal form, multiply the number by 100 to get 0. 37. Do the same for all the percentages in the problem.
By dividing the total items represented by percentages by the overall number of items, you can determine the average percentage. Out of a total of 500 pencils, 200 were taken out of the example. Divide 200 by 500, which is equal to 0. 40. Convert to percentage form by multiplying 0. 40 by 100. The average percentage removed equals 40 percent.
To determine the actual number of items that each category’s percentage represents, multiply the percentage for each category by the overall number of items in each category. Say, for instance, that 0 out of 200 red pencils in a box, or 37%, have been taken out. 37 x 200, or 74 red pencils removed. Assume that 42 percent of the 300 blue pencils in a box have also been taken out. That means 0. 42 x 300, or 126 blue pencils, have been removed.
Averaging percentages is rarely as simple as adding and dividing them as it is with other types of numbers. You must take into account the base numbers in order to determine the percentage average because the numbers that each percentage represents may differ, for example, 10 percent of a large group of people compared to 12 percent of a small group.
A percentage is a proportion or ratio that indicates how many parts are in one hundred. For instance, if a box of 100 pencils contains 40% red pencils, that means 40% of the pencils in the box are red. 40 percent indicates that only eight of the twenty pencils in the second box are red.
3 Suitable Ways to Calculate Average Percentage in Excel
The following three techniques can be used to determine the average percentage. Whatever the methods, the output will be the same. We will use mathematical formulas and the functions SUMPRODUCT, SUM, and AVERAGE to calculate average percentages. Here’s an overview of the dataset for today’s task.
FAQ
How do you find the average of 8 percentages?
- First, sum all of the percentages together. Add all of the percentages together to get one value.
- Next, count the number of values. This is the total number of values.
- Calculate the average. To determine the average, enter the data into the formula above.
What are the 3 ways to calculate average?
The three primary averages are mean, median, and mode. Each of these methods operates slightly differently and frequently yields generally different values. The mean is the most commonly used average. You add up all the values and divide this sum by the total number of values to obtain the mean value.
