How to Find the Average of a Group of Numbers

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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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  1. The first thing you need to do is to add up all of the numbers in the set. [1] Let's say you're working the following set of numbers: 1, 2, 3, and 6. . [2]
  2. 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. . [3] The average of the group of numbers is 3. [4]
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Part 2
Part 2 of 2:

Finding the Weighted Average

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  1. 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] 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]
    • Homework average = 93%
    • Test average = 88%
    • Quiz average = 91 %
  2. Remember that the weight categories should add up to 100%. [7] Let's say you're working with the following weight categories: [8]
    • Homework average = 30 % of final grade
    • Test average = 50 % of final grade
    • Quiz average = 20 % of final grade
  3. 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] Now, multiply these decimal-converted weight categories by the averages they represent. [10]
    • Homework average =
    • Test average =
    • Quiz average =
  4. [11] To find the final weighted average, simply add up the three results. . The final weighted average of the three groups of numbers is . [12]
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  • Question
    The average of 4 numbers is 56. If the average of 3 of the numbers is 52, what is the 4th number?
    Donagan
    Top Answerer
    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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    Not Helpful 5 Helpful 28
  • Question
    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?
    Community Answer
    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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  • Question
    How do I find the average of 4kg, 240g, and 167g?
    Community Answer
    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.
    Thanks! We're glad this was helpful.
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      References

      1. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2020.
      2. ↑ https://www.omnicalculator.com/math/average
      3. ↑ https://www.mathsisfun.com/mean.html
      4. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2020.
      5. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2020.
      6. ↑ https://www.indeed.com/career-advice/career-development/how-to-calculate-weighted-average
      7. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2020.
      8. ↑ https://www.omnicalculator.com/math/weighted-average
      9. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2020.
      1. ↑ https://sciencing.com/calculate-grades-weighted-percentages-7648649.html
      2. ↑ https://www.omnicalculator.com/math/weighted-average
      3. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2020.

      About This Article

      Article Summary X

      To determine an average, first add together all the numbers in the set. For example, if your set is 1, 2, 3, and 4, you would add all of those numbers together to get 10. Next, count how many numbers are in the set - in this case, 4. Divide your sum by the amount of numbers in the set. The result is your answer. Keep reading the article if you want to learn how to find a weighted average!

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