How to Find the Average of a Group of Numbers

• 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.

Finding the Average

Find the sum of the numbers in the set. The first thing you need to do is to add up all of the numbers in the set. Let's say you're working the following set of numbers: 1, 2, 3, and 6. 1 + 2 + 3 + 6 = 12 {\displaystyle 1+2+3+6=12} 1+2+3+6=12.

Divide the result by the amount of numbers in the set. 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 {\displaystyle 12/4=3} 12/4=3. The average of the group of numbers is 3.

Finding the Weighted Average

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. 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: Homework average = 93% Test average = 88% Quiz average = 91 %

Write down the weight category of each average. Remember that the weight categories should add up to 100%. Let's say you're working with the following weight categories: Homework average = 30 % of final grade Test average = 50 % of final grade Quiz average = 20 % of final grade

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. Now, multiply these decimal-converted weight categories by the averages they represent. Homework average = 93 x .3 = 27.9 {\displaystyle 93x.3=27.9} 93x.3=27.9 Test average = 88 x .5 = 44 {\displaystyle 88x.5=44} 88x.5=44 Quiz average = 91 x .2 = 18.2 {\displaystyle 91x.2=18.2} 91x.2=18.2

Add the results. To find the final weighted average, simply add up the three results. 27.9 + 44 + 18.2 = 90.1 {\displaystyle 27.9+44+18.2=90.1} 27.9+44+18.2=90.1. The final weighted average of the three groups of numbers is 90.1 {\displaystyle 90.1} 90.1.

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