How to Find the Average of a Group of Numbers

Co-authored by Mario Banuelos, PhD

Last Updated: November 29, 2022 Fact Checked

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If you have a list of numbers, or a set, you can use the numbers to find an average, which is a central point in the group. In everyday life, you might need to calculate an average to estimate your monthly expenses, find out about how much time it usually takes to accomplish a task, or determine the rough size of a crowd based on previous attendance.

Things You Should Know

To find the average, find the sum of all the numbers and divide the result by the amount of numbers in the set.
For the weighted average, find the average of each category and the weight category of each average.
Then, multiply each average by its weight category and add the results to find your answer.

Part 1

Part 1 of 2:

Finding the Average

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The first thing you need to do is to add up all of the numbers in the set.^{[1]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2020.} Let's say you're working the following set of numbers: 1, 2, 3, and 6. $1+2+3+6=12$ .^{[2]
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Research source}
There are 4 distinct numbers in the set. So, take the sum of the numbers, 12, and divide it by 4 to get the average. $12/4=3$ .^{[3]
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Research source} The average of the group of numbers is 3.^{[4]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2020.}

Part 2

Part 2 of 2:

Finding the Weighted Average

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1
Write down the average of each category. Use the method of finding the average -- adding up all of the numbers in the set and dividing the result by the amount of numbers -- to find the average of each category.^{[5]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2020.} Let's say you're trying to find your weighted average for a class and you're working with the following averages and weight categories:^{[6]
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Research source}
- Homework average = 93%
- Test average = 88%
- Quiz average = 91 %
2
Write down the weight category of each average. Remember that the weight categories should add up to 100%.^{[7]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2020.} Let's say you're working with the following weight categories:^{[8]
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Research source}
- Homework average = 30 % of final grade
- Test average = 50 % of final grade
- Quiz average = 20 % of final grade
3
Multiply each average by its weight category. Now, simply convert each weight category into a decimal and then multiply it by the average it represents. 30% is really .3, or 3/10 of the final grade, 50% is really .5, or 1/2 of the total grade, and 20% is really .2, or 2/10 of the final grade.^{[9]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2020.} Now, multiply these decimal-converted weight categories by the averages they represent.^{[10]
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Research source}
- Homework average = $93x.3=27.9$
- Test average = $88x.5=44$
- Quiz average = $91x.2=18.2$
^{[11]
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Research source} To find the final weighted average, simply add up the three results. $27.9+44+18.2=90.1$ . The final weighted average of the three groups of numbers is $90.1$ .^{[12]
X
Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2020.}

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The average of 4 numbers is 56. If the average of 3 of the numbers is 52, what is the 4th number?

Donagan

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The sum of the four numbers is 4 x 56. The sum of the three numbers is 3 x 52. The difference between the those two sums is the fourth number.

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If the average age of three brothers is 15, and two brothers are 15 and 12, how do I find the age of the third brother?

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15 times 3 equals 45, 12 plus 15 equals 27, 45 minus 27 equals 18. The third brother's age is 18. Check: 15 plus 12 equals 27, 27 plus 18 equals 45, and 45 divided by 3 equals 15.

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How do I find the average of 4kg, 240g, and 167g?

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To find the average, add all of the numbers in the set. In your case, 4000, because 1kg+1000g, 4000+240+167 = 4407. Then, because there are three numbers, divide by 3 4407/3 = 1469.

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