MATH CALCULATOR
Average Calculator for Mean, Median and Mode
Calculate the average, or arithmetic mean, of a list of numbers and quickly find the median, mode, sum, minimum, maximum, and range of your data.
Calculate Your Statistics
Calculate the mean, median, mode, sum, and range of a set of numbers.
Enter Your Numbers
Quick Example
Results update when you click Calculate.
Calculation Summary
Key statistics for your data set.
| Statistic | Result |
|---|---|
| Number of values | 5 |
| Sum | 90 |
| Mean / Average | 18 |
| Median | 18 |
| Mode | No mode |
| Minimum | 12 |
| Maximum | 25 |
| Range | 13 |
Values at a Glance
Your values sorted from smallest to largest.
How the Average Is Calculated
What Is an Average?
An average is a single value used to represent the typical or central value of a group of numbers. The most common type of average is the arithmetic mean, which is calculated by adding all of the values together and dividing the total by the number of values.
For example, if five test scores are 70, 75, 80, 85, and 90, their average is 80. The average gives you a quick way to summarize the overall level of the data.
Average Formula
To calculate an arithmetic mean, add all of the numbers and divide the sum by the number of values.
For example, the average of 10, 20, 30, 40, and 50 is calculated as 150 ÷ 5 = 30.
Mean, Median, and Mode
The mean is only one way to describe the center of a data set. The median and mode can provide useful additional information, especially when the values are unevenly distributed.
| Statistic | What It Means | Example |
|---|---|---|
| Mean | Sum of all values divided by the count | 10, 20, 30 → 20 |
| Median | Middle value after sorting the data | 10, 20, 30 → 20 |
| Mode | Value that occurs most frequently | 10, 20, 20, 30 → 20 |
How to Calculate an Average
Calculating an average is straightforward. First, add every number in the data set. Next, count how many numbers there are. Finally, divide the total by the number of values.
- Add all of the numbers.
- Count the number of values.
- Divide the sum by the count.
- Round the result if appropriate.
For example, suppose your values are 12, 15, 18, 20, and 25. Their sum is 90 and there are five values, so the average is 90 ÷ 5 = 18.
Average Example
| Value | Position |
|---|---|
| 12 | 1 |
| 15 | 2 |
| 18 | 3 |
| 20 | 4 |
| 25 | 5 |
| Sum = 90 | Count = 5 |
| Average = 18 | 90 ÷ 5 |
Average vs. Median
The mean and median can produce different results when a data set contains unusually large or small values. The mean uses every value in the calculation, while the median depends on the middle position after the values are sorted.
For example, consider 10, 12, 14, 16, and 100. The mean is 30.4, while the median is 14. The large value of 100 pulls the mean upward. In situations like this, the median can sometimes provide a better description of the typical value.
What Is the Range?
The range measures the spread between the smallest and largest values in a data set. It is calculated by subtracting the minimum value from the maximum value.
If the smallest value is 12 and the largest value is 25, the range is 13.
When Should You Use an Average?
Averages are useful whenever you need to summarize several numerical observations with one representative value. Common examples include grades, test scores, monthly expenses, temperatures, measurements, performance metrics, and business statistics.
If your data includes percentage changes, use the percentage calculator to compare values. For proportional quantities, the ratio calculator offers another way to compare parts.
Average and Fractions
An average does not always have to be a whole number. For example, the average of 2, 3, and 4 is 3, while the average of 2, 3, and 5 is 3.333... For exact results, use the fraction calculator for fraction operations and conversions.
Average and Standard Deviation
The average describes the center of a data set, but it does not tell you how tightly the values are grouped around that center. Standard deviation provides additional information about the spread of the data.
If you need to understand both the average and the variability of a data set, the measure data variability can help you explore how widely the values vary.
How to Use This Average Calculator
Enter your numbers in the input box. You can separate values with commas, spaces, semicolons, or line breaks. Then select Calculate Average to calculate the mean and other statistics.
- Enter the numbers you want to analyze.
- Separate each value with a comma, space, or new line.
- Click Calculate Average.
- Review the mean, median, mode, sum, and range.
Average Calculator Tips
- Check that all of the intended values were entered.
- Remember that a large outlier can significantly affect the mean.
- Compare the mean and median when the data is unevenly distributed.
- Use the range to get a quick sense of the spread between the smallest and largest values.
- Use standard deviation when you need a more detailed measure of variability.
Frequently Asked Questions
How do I calculate an average?
Add all of the numbers together and divide the sum by the number of values. For example, 10 + 20 + 30 equals 60, and 60 ÷ 3 equals 20.
Is average the same as mean?
In many everyday and mathematical contexts, average refers to the arithmetic mean. The mean is calculated by dividing the sum of the values by their count.
What is the median?
The median is the middle value after the numbers are arranged from smallest to largest. If there are an even number of values, the median is the average of the two middle values.
What is the mode?
The mode is the value that occurs most frequently in a data set. A data set can have one mode, multiple modes, or no mode.
Can an average be a decimal?
Yes. An average does not need to be a whole number. For example, the average of 2, 3, and 5 is 3.333...
What happens if every number is different?
The data set has no mode if every value occurs only once. The mean and median can still be calculated.
Does a large number affect the average?
Yes. Because the mean uses every value, an unusually large or small number can move the average significantly.
What is the difference between mean and median?
The mean uses the sum of every value, while the median uses the middle position after sorting the values. The median is often less affected by extreme values.