# How to find the average of a group of numbers

To find the basic average of a group of numbers, all you have to do is add them together and divide the result by the number of numbers there are. Pythagoras aside, there's a new math genius on the team - that's right!

## Steps

### Part 1 of 2: Finding the Average

#### Step 1. Find the sum of the numbers in total

The first thing you have to do is add all the numbers there are. Let's say you work with the following group of numbers: 1, 2, 3, and 6. So, 1 + 2 + 3 + 6 = 12.

#### Step 2. Divide the result by the number of numbers in all

There are four different numbers in the group. So, take the sum of numbers (12) and divide it by 4 to get the average. So, 12/4 = 3. The average of the group of numbers will be 3.

### Part 2 of 2: Finding the Weighted Average

#### Step 1. Record the average for each category

Use the method of finding the average (adding all the numbers there are and dividing the result by the number of numbers) to determine the average for each category. Let's say you're trying to find the weighted average for a class and you're working with the following weight categories and averages:

• average of tasks = 93%
• test average = 88%
• exam average = 91%

#### Step 2. Write down the weight category of each average

Remember that the weight categories must add up to 100%. Let's say you work with the following weight categories:

• test average = 50% of the final grade
• exam average = 20% of the final grade

#### Step 3. Multiply each average by its weight category

Now just convert each weight category to a decimal and then multiply it by the average it represents. 30% is actually 0, 3 or 3/10 of the final grade; 50% is actually 0, 5 or 1/2 of the final grade and 20% is actually 0, 2 or 2/10 of the final grade. Then multiply those weight categories converted to decimals by the averages they represent.

• average homework = 93 x 0.3 = 27.9
• test average = 88 x 0.5 = 44.00
• exam average = 91 x 0.2 = 18.2

#### Step 4. Add the results

To find the final weighted average, simply add the three results. So, 27.9 + 44.00 + 18.2 = 90.1. The final weighted average of the three groups of numbers is 90.1.