How Do You Find The Average Of Percentages?

Knowing how to find the average of percentages is a basic life skill that comes in handy across various life scenarios – the best formula to use changes depending on the situation to get the most accurate answer possible.

Customarily, percentages are used to calculate figures like sales tax. However, their use is much more expansive and can also be applied to business factors, such as online analytics. This broad scope of potential uses makes it a practical skill to master.

Key Takeaways:

• It is important to know how to calculate average percentages in both your professional and personal life.

• Percentages are used all the time in the real world, from tipping to sales at stores.

• Averages play an important role in creating a useful value out of large sets of data, especially in areas like scientific research and sports.

• To calculate average percentage, add all percentages together as numbered values and divide by the sum of all the sets. Then multiply by 100.

The Average Percentage Formula

At first glance, the average percentage formula is intimidating. Once you understand the breakdown of each step, though, it becomes much easier.

What this says is that you need to first find the number value of each percentage in question. Then you add all your percentages as number values together. Divide them by the sum of your sample sets, where each sample set correlates to a percentage. After that, you multiply the answer by 100 to get your average percentage.

Note that to calculate average percentage, we must convert our percentages into a numbered value.

To find the number value of percentage1, you must convert the percentage into a decimal and then multiply the decimal by the sample size of that percentage. For example, lets say you have 200 apples. 25% of those apples are rotten. 25% as a decimal is 0.25. Multiply 0.25 by 200 and you get 50. So 25% of 200 apples equal 50 apples. 50 is your number value of your percentage.

To make more sense of this process, lets break it into steps.

Steps for Finding the Average of Percentages

Lets look at an example to put the steps of finding an average percentage into action.

In this example we have enough information to calculate the average percentage of all bakery items sold.

1. Convert all percentages to decimals. Once you’ve grazed through the formula and gotten thoroughly stressed out about the prospect of solving it, it’s time to jump into the steps. The percentages that you’re working with need to be turned into decimals before continuing to any other part of the calculation.

   To turn a percentage into a decimal, divide it by 100.

   Going back to the earlier example of the bakery, we’d need to convert the percentages of cookies and cupcakes sold back into decimals by dividing by 100. The result is 0.85 and 0.74.

2. Determine the number that each decimal represents. The first stages of averaging percentages are all about making the values compatible with the formula. Now that you’ve arrived at a decimal version of the percentage, it needs to become a whole number.

   To turn a converted decimal into a whole representative number to plug into the formula, multiply the decimal by the sample set value it coincides with.

   In the bakery example, we would multiply 0.85 by 800 and 0.74 by 450 to arrive at their representative whole numbers. The resulting values would be 680 cookies and 333 cupcakes. These are the actual number of cookies and cupcakes sold that week.

3. Add the representative whole number results together. We’ve gotten past the most confusing portion of finding the average percentage. Finishing the equation is just a matter of adding and plugging in results.

   First, add together the representative whole numbers.

   At the bakery, the representative whole numbers would be 680 and 333, each respectively representing the number of cookies and cupcakes sold that week. After adding these two numbers together, the result is 1,013. This is the total number of items sold.

4. Add together the sample set numbers. The second bracket of numbers to add is the values of the sample set. This is the total number of items that are being examined in each category.

   The result goes on the bottom of the division equation in the average percentage formula.

   The sample sets are the number of total cookies and cupcakes made in that week in the bakery. These values are 800 cookies and 450 cupcakes. After adding these together, we arrive at the value of 1,250. This is the total number of items made.

5. Plug into the formula and solve. The final step towards solving the equation is to plug in all the values to the original average percentage formula and solve. Simple enough.

   As a reminder, the formula is:

   [(Number Value of Percentage1 + Number Value of Percentage2 + Number Value of PercentageN…)/(size of sample set1 + size of sample set2 + size of sample setN…)] X 100 = Average Percentage

   Finishing up the example of the bakery, we fill in the values for the number of items sold and the number of items made. Then, divide the two numbers and multiply the result by 100 to arrive at the average percentage between cookies and cupcakes sold in a week.

   ((1,013)/(1,250))= 0.8104

   0.8104 X 100 = 81.04

   The average percentage of items sold at the bakery is 81.04%.

What Are Percentages?

A percentage is a term used to describe portions out of the total amount of 100. Often, this is used to create a more vivid picture of a decimal number. Calculating percentages is usually first introduced as a math concept in early education, but many people haven’t had much experience with it since then.

This causes a deficit in percentage average knowledge, and most adults need some reminders of how to perform the process.

Real-World Uses of Percentages

We’re all familiar with the groan of a middle school classroom who insists that they’ll never need the math equations they learned – muffling out the sound of their teacher insisting that it’s going to be handy for them to know someday.

To prove those middle-schoolers wrong, below are some examples of real-world uses for percentages and formulas involving them:

1. Earning commission at your job. Many people earn a commission from the sales they make at their job as a part of their benefits. The commission value is an agreed-upon percentage of the total sale, which is the amount the salesperson receives.

   Knowing how to solve for percentages in these roles ensures you’ll receive the correct amount for each sale made.

2. Tipping at restaurants. This is probably the most popular example of when people use percentages in their daily life. Tipping is customary in the United States, and failing to provide an appropriate tip leaves servers feeling agitated.

   Knowing how to convert a percentage from a whole number is how you arrive at the correct amount of tip to leave.

3. Sales at stores. Everybody enjoys a special markdown on a popular item. It’s common to see retailers list their sales in the form of percentages, as opposed to expressing how much money you’ll actually need to pay for the item.

   This leaves the customer to figure out what the actual discount is from the percentage value.

4. Interest. Interest on credit cards and savings accounts is a factor that has an enormous impact on an adult’s financial health. Many people come across percentage values of interest rates when applying for credit or are considering a savings account that accrues interest over time.

   However, understanding the mathematical conversions behind these percentages is important to know how much interest debt is owed or payable to you exactly.

What Is an Average in Mathematics?

An average in mathematics is the middle point in a set of numbers. It’s a fairly simple calculation that’s achieved by adding all the factors together and dividing the result by the number of items in the set.

For example, consider a business that wants to find their average monthly income over the past six months.

Their income for each month is: $1,500, $2,000, $1,200, $3,700, $2,600, $3,100

After adding these monthly incomes together, the result is a total of $14,100.

This number is divided by the six months in question to get an average income of $2,350.

This is the most basic form of using averages in mathematics. However, this isn’t the most reliable manner of finding an average when dealing with large numbers or high variance across the set.

Real-World Uses of Averages

Similar to percentages, there are surprisingly a lot of real-world uses for averages. Below are a few examples:

1. Athlete’s statistics. Professional sports are one of the world’s favorite pastimes. Think about the players on your favorite teams and what their sports statistics look like. For basketball, this might be a shooter’s average number of baskets made.

   This value describes the mean number for how many times the player is successful in their attempt to shoot a basket.

2. A student’s grade point average. A student’s grade point average, or GPA, is an ideal example of an average. The value of their GPA is the average scores they’ve received out of the total possible points they could’ve gotten, with a 4.0 being the highest.

3. Scientific research. The science and mathematics disciplines often go hand in hand. The use of averages and their equations is an example of this. Scientific research across many subjects uses averages to understand the data that they’ve collected through research.

Examples of Average Calculators to Use

Sometimes, you don’t have the time or brain space to calculate the average percentage through mental math. When this happens, some excellent average calculators are used to make life a little easier.

Below are the best examples of average calculators:

1. Omni average calculator. This is a recommended average calculator to use. It allows you to input up to thirty numbers. Additionally, the website provides a calculator for other basic mathematics functions and formulas, such as absolute value and long division.

2. Calculator soup average calculator. This average calculator has an old school interface, but it gets the job done when it comes to calculating. The website also provides guidelines for solving averages by hand, in case you ever need a refresher.

3. Rapid Tables average calculator. Rapid Table’s average calculator is similar to the others offered on this list, but the website offers so much more than just average calculation.

   Its computing system accounts for additional factors in a set, such as standard deviation and range. Plus, about 30 other kinds of calculators at your disposal solve for anything from trigonometry to roots.

Author

Sky Ariella

Sky Ariella is a professional freelance writer, originally from New York. She has been featured on websites and online magazines covering topics in career, travel, and lifestyle. She received her BA in psychology from Hunter College.