Average Calculator
An average is one of the most useful numbers in everyday life, and also one of the most misunderstood. It appears in test scores, sports statistics, monthly spending, exam grades, temperatures, salaries and product ratings, and each time it promises a single number that sums up a whole set of values. The trouble is that there is more than one kind of average, and the kind you choose changes the answer — sometimes dramatically. The mean adds everything up and divides by the count, the median picks the middle value, and the mode picks the most common value, and each one tells a different story about the same data. This free average calculator works out all three at once, together with the count, the sum, the range and the standard deviation, so you can see the full picture instead of guessing which average fits. Paste in a list of numbers separated by commas, spaces or line breaks, tap Calculate, and the results appear instantly. Everything runs in your browser with nothing to install and no account to create.
Your Average Results
—
How to Use This Calculator
- Enter your numbers in the box, separated by commas, spaces or line breaks. Decimals and negative numbers are fine.
- Tap Calculate. The mean, median, mode, range and both standard deviations appear below.
- Read the mean first for a general summary, then check the median to see whether a few extreme values are pulling the mean away from the typical value.
- Use the mode when you want the most common answer, such as the most common shoe size or the most frequent test score.
Understanding Mean, Median, Mode and Spread
The mean is the average most people mean when they say "average": add all the numbers together and divide by how many there are. For 4, 8, 15, 16, 23 and 42 the sum is 108 and there are 6 numbers, so the mean is 108 ÷ 6 = 18. The mean uses every value, which is a strength and a weakness: one very large number can drag it upward, so a class where most students score 70 but one scores 100 will have a mean above what most students actually achieved.
The median is the middle value when the numbers are sorted from smallest to largest. With an odd count it is the single middle number; with an even count it is the average of the two middle numbers. For our example the sorted list is 4, 8, 15, 16, 23, 42, the two middle numbers are 15 and 16, and the median is (15 + 16) ÷ 2 = 15.5. The median, 15.5, is lower than the mean, 18, because the large value 42 pulls the mean up while leaving the median almost untouched. That is why house prices and incomes are usually reported as medians.
The mode is the value that appears most often. A set can have one mode, several modes, or no mode at all — our example has no mode, because every number appears exactly once. The range, the largest value minus the smallest, is the simplest measure of spread: here it is 42 − 4 = 38. Standard deviation measures how far the numbers typically sit from the mean. The population version divides by the number of values and is about 12.32 for this set; the sample version divides by one less than the count and is about 13.49. Use the population figure when your numbers are the whole group, and the sample figure when they are a sample from a larger group.
Worked Example
Example — the numbers 4, 8, 15, 16, 23, 42: First, count them: there are 6 numbers. Add them: 4 + 8 + 15 + 16 + 23 + 42 = 108. The mean is 108 ÷ 6 = 18. Sort them (they are already sorted) and take the two middle values, 15 and 16: the median is (15 + 16) ÷ 2 = 15.5. Every value appears once, so there is no mode. The smallest value is 4 and the largest is 42, so the range is 42 − 4 = 38. For the standard deviation, subtract the mean 18 from each value to get −14, −10, −3, −2, 5 and 24; square them to get 196, 100, 9, 4, 25 and 576; add those to get 910; divide by 6 for the population variance 151.67 and take the square root to get about 12.32; divide by 5 instead for the sample variance 182 and take the square root to get about 13.49.
Example — why the median matters: Imagine five salaries: $40,000, $45,000, $50,000, $55,000 and $500,000. The mean is $138,000, which describes nobody in the group, while the median is $50,000, the middle salary.
Frequently Asked Questions
What is the difference between mean, median and mode?
The mean is the sum of all the numbers divided by how many there are. The median is the middle value when the numbers are sorted. The mode is the value that appears most often. For 4, 8, 15, 16, 23, 42 the mean is 18, the median is 15.5 and there is no mode.
When should I use the median instead of the mean?
Use the median when a few very large or very small values would distort the mean. House prices are a classic example: one mansion can pull the mean far above what a typical home costs, while the median stays close to the middle home.
What is the difference between population and sample standard deviation?
Population standard deviation divides by the number of values and describes a complete set. Sample standard deviation divides by one less than the number of values and estimates the spread of a larger group from a sample. For 4, 8, 15, 16, 23, 42 the population value is about 12.32 and the sample value is about 13.49.
How do I enter my numbers?
Type or paste them into the box, separated by commas, spaces or line breaks. Decimals and negative numbers are accepted. The calculator ignores extra commas and blank lines, so you can paste a column of numbers straight from a spreadsheet.
What does the range tell me?
The range is the largest value minus the smallest value, so it shows how far apart the extremes are. For 4, 8, 15, 16, 23, 42 the range is 42 - 4 = 38. It is a quick measure of spread, but it only uses two values, so it can be affected by a single outlier.