Average Calculator
Use this free Average Calculator to find the arithmetic mean, median, mode, range, sum, count, minimum and maximum of a list of numbers. Enter numbers separated by commas, spaces or new lines to calculate the average instantly.
Calculate Average, Mean, Median & Mode
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What Is an Average?
An average is a number used to represent the central or typical value of a group of numbers. In everyday mathematics, the word "average" usually refers to the arithmetic mean.
To calculate the arithmetic mean, add all the numbers together and divide the total by the number of values. For example, the average of 10, 20, 30, 40 and 50 is 30.
However, "average" can refer to different measures of central tendency. The mean, median and mode can give different results for the same data set. This calculator shows all three so you can better understand your numbers.
Average Formula
The mathematical formula for the arithmetic mean is:
Where x̄ is the mean, Σx is the sum of all values, and n is the number of values.
Mean, Median, Mode and Range
| Measure | What It Means | How It Is Calculated |
|---|---|---|
| Mean | The arithmetic average of all values. | Sum of values ÷ number of values. |
| Median | The middle value after sorting the numbers. | Use the middle number, or average the two middle numbers if the count is even. |
| Mode | The value that occurs most frequently. | Find the value or values with the highest frequency. |
| Range | The difference between the largest and smallest values. | Maximum − Minimum. |
How to Calculate an Average
Calculating an arithmetic average is straightforward. Follow these steps:
- Write down all the numbers in the data set.
- Add all the values together to find the sum.
- Count how many numbers are in the data set.
- Divide the total sum by the number of values.
- The result is the arithmetic mean or average.
Average Example
Suppose the numbers are:
First calculate the sum:
There are five numbers, so:
Therefore, the arithmetic mean of the five numbers is 30.
How to Calculate the Median
The median is the middle value after a data set has been arranged from smallest to largest.
Odd Number of Values
If there are an odd number of values, there is one value exactly in the middle.
Median = 12
Even Number of Values
If there are an even number of values, take the average of the two middle values.
Median = (8 + 12) ÷ 2 = 10
How to Calculate the Mode
The mode is the number that appears most often in a data set.
Mode = 7
A data set can have more than one mode. If two or more values have the same highest frequency, the data set can be described as bimodal or multimodal.
If every number occurs only once, there is no mode.
How to Calculate the Range
The range measures the difference between the largest and smallest values in a data set.
For example, if the numbers are 10, 15, 20, 35 and 50:
Mean vs Median: Which Should You Use?
The mean uses every number in the data set, so it can be strongly affected by extremely large or small values. The median is based on position and is generally less affected by outliers.
For example, consider these values:
The very large value of 200 pulls the mean upward, while the median remains 22. In data sets with significant outliers, the median may provide a more representative description of the typical observation.
Common Average Examples
| Numbers | Sum | Count | Average |
|---|---|---|---|
| 10, 20, 30 | 60 | 3 | 20 |
| 5, 10, 15, 20 | 50 | 4 | 12.5 |
| 70, 80, 90 | 240 | 3 | 80 |
| 12, 15, 18, 21, 24 | 90 | 5 | 18 |
| 100, 200, 300, 400 | 1,000 | 4 | 250 |
Average Calculator for Test Scores and Grades
Students can use an average calculator to calculate the average of test scores, exam marks, quiz results and assignment grades.
For example, if five test scores are 70, 75, 80, 85 and 90:
Average = 400 ÷ 5 = 80
Note that a simple average is appropriate only when each score contributes equally. If assignments or exams have different weights, a weighted average should be used instead.
Average Calculator for Prices
An average can also be used to calculate the typical price across several purchases, products or transactions.
For example, if five items cost $10, $15, $20, $25 and $30:
The arithmetic average gives an equal contribution to every price. For financial or business analysis, a weighted average may be more appropriate when transaction quantities differ.
Average Calculator for Salary and Income
Average calculations are frequently used to summarize salaries, wages, household income and other financial data.
However, income data can contain very high values that significantly increase the arithmetic mean. For this reason, analysts may compare the mean with the median when describing a typical income.
Average vs Percentage
An average and a percentage are different types of calculations. An average summarizes a group of numerical values, while a percentage expresses a value as a proportion out of 100.
For example, the average of 70, 80 and 90 is 80. A percentage calculation could instead determine what percentage one value represents of another.
Use the Percentage Calculator when you need percentage calculations.
Average vs Weighted Average
A simple arithmetic mean gives every value equal importance. A weighted average gives different values different levels of importance.
Weighted averages are commonly used for course grades, investment returns, inventory costs and other situations where observations do not have equal importance.
When Should You Use an Average Calculator?
- Calculate the average of school or university marks.
- Find the average of test and exam scores.
- Calculate average prices or costs.
- Find average sales values.
- Calculate average salary or income.
- Analyze sports scores and performance.
- Summarize measurements and experimental data.
- Compare groups of numerical data.
- Find the median or mode of a data set.
- Find the range between the highest and lowest values.
Average Calculator Accuracy
The calculator performs the arithmetic directly in your browser using JavaScript. It accepts positive numbers, negative numbers and decimal values.
The displayed result is rounded for readability, while the calculation is performed using the entered numerical values. Very large or extremely precise numbers can eventually be affected by the numerical precision limitations of standard JavaScript floating-point arithmetic.
Frequently Asked Questions
In everyday mathematics, average usually means the arithmetic mean: add all values together and divide the sum by the number of values.
Add all numbers in the data set and divide the total by the number of values. The formula is: Mean = Sum of values ÷ Number of values.
The mean is the sum of all values divided by the number of values. The median is the middle value after the numbers are sorted, or the average of the two middle values when there is an even number of values.
The mode is the value or values that occur most frequently in a data set. A data set can have one mode, multiple modes or no mode.
The range is the largest value minus the smallest value in a data set.
Yes. An arithmetic mean can be a decimal even when all of the original values are whole numbers.
Yes. If multiple values share the highest frequency, the data set can have two or more modes.
The median can be more representative when a data set contains extreme values or outliers because the median is less affected by unusually large or small observations.
The data set has no mode because no value occurs more frequently than another.
The sum is 150 and there are 5 numbers, so the arithmetic mean is 150 ÷ 5 = 30.
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