How to Calculate Average of Negative and Positive Numbers

Calculating the average of numbers that include both negative and positive values follows the same basic principle as calculating an average of only positive numbers. The average (or arithmetic mean) is simply the sum of all numbers divided by the count of numbers. This method works regardless of whether the numbers are positive, negative, or a mix of both.

What is an average?

The average, also known as the arithmetic mean, is a measure of central tendency that represents the typical value in a dataset. It's calculated by adding up all the values and then dividing by the number of values. This gives you a single number that summarizes the central point of the data.

For example, if you have test scores of 85, 90, and 75, the average would be (85 + 90 + 75) / 3 = 83.33. This tells you that, on average, the test scores are around 83.33.

Average formula

The formula for calculating the average (arithmetic mean) is:

Average = (Sum of all numbers) / (Count of numbers)

Where:

Sum of all numbers - Add up all the numbers in your dataset
Count of numbers - The total number of values in your dataset

This formula works the same way whether you're dealing with positive numbers, negative numbers, or a mix of both.

How to calculate average

Calculating the average of numbers that include negative values follows these steps:

List all the numbers you want to average
Add them together to get the sum
Count how many numbers you have
Divide the sum by the count to get the average

Important: The average can be negative if the sum of all numbers is negative. This simply means that, on average, the numbers are below zero.

Examples with negative numbers

Here are some examples showing how to calculate averages with negative numbers:

Example 1: Simple case

Numbers: 5, -3, 2

Calculation: (5 + (-3) + 2) / 3 = (4) / 3 ≈ 1.33

Interpretation: The average is 1.33, which is positive because the positive numbers outweigh the negative ones.

Example 2: Negative average

Numbers: -4, -1, -2

Calculation: (-4 + (-1) + (-2)) / 3 = (-7) / 3 ≈ -2.33

Interpretation: The average is -2.33, which is negative because all numbers are negative.

Example 3: Mixed numbers

Numbers: 10, -5, 3, -2

Calculation: (10 + (-5) + 3 + (-2)) / 4 = (6) / 4 = 1.5

Interpretation: The average is 1.5, which is positive because the positive numbers outweigh the negative ones.

Numbers	Sum	Count	Average
5, -3, 2	4	3	1.33
-4, -1, -2	-7	3	-2.33
10, -5, 3, -2	6	4	1.5

FAQ

Can the average be negative?

Yes, the average can be negative if the sum of all numbers in your dataset is negative. This simply means that, on average, the numbers are below zero.

Do I need to treat negative numbers differently when calculating the average?

No, you treat negative numbers the same way as positive numbers when calculating the average. Just add them together normally and divide by the count.

What if I have a mix of positive and negative numbers?

The calculation remains the same. Add all numbers together (including the negatives) and divide by the count. The result will be positive if the positive numbers outweigh the negatives, and negative if the negatives outweigh the positives.

Is the average the same as the median?

No, the average (mean) and median are different measures of central tendency. The median is the middle value when numbers are ordered, while the average is the sum divided by the count. They can give different insights about your data.