Average Calculator
Paste or type a list of numbers to get their mean (the usual average), median and mode, together with the sum, range and standard deviation. The sum and mean are exact, so decimals add up correctly.
Separate numbers with spaces or new lines; use a dot for decimals. Up to 2,000 numbers.
Result
Enter some numbers to see their average.
The calculation runs in this browser tab. Nothing you enter is uploaded, saved or logged.
What is an average?
“Average” most often means the arithmetic mean: add the numbers and divide by how many there are. The mean of 2, 4 and 9 is (2 + 4 + 9) ÷ 3 = 5. It uses every value, which also makes it sensitive to extreme ones.
Two other averages answer different questions. The median is the middle value once the numbers are sorted (the mean of the two middle values when there is an even count), and it barely moves when one value is extreme, which is why it is used for incomes and house prices. The mode is the value that appears most often. The standard deviation measures how spread out the numbers are around the mean.
How to use the Average Calculator
- Enter your numbers, separated by spaces or new lines. Use a dot for decimals; a comma is accepted only when followed by a space.
- The mean appears as you type, with the count, sum, median, mode, minimum, maximum and range below it.
- Both standard deviations are shown: population (the list is everything) and sample (the list is a sample from a larger group).
- Use Copy result to copy the mean, or Reset to clear the list.
Formula
- Mean
- mean = (x₁ + x₂ + … + xₙ) ÷ n
- Median
- the middle value of the sorted list; for an even count, the mean of the two middle values
- Population standard deviation
- σ = √( Σ(xᵢ − mean)² ÷ n )
- Sample standard deviation
- s = √( Σ(xᵢ − mean)² ÷ (n − 1) )
Use the sample formula when the numbers are a sample drawn from a larger population (the usual case in surveys and experiments), and the population formula when the list contains every value of interest. The sample version needs at least two numbers.
When several values tie for most frequent, all of them are listed. When every value appears once, there is no mode.
Worked example
A classic data set of eight numbers. The mean is 5, the median 4.5 and the mode 4:
| Question | Result |
|---|---|
| Input: Numbers | 2, 4, 4, 4, 5, 5, 7, 9 |
| Mean (average) | 5 |
| Count | 8 |
| Sum | 40 |
| Median | 4.5 |
| Mode | 4 (appears 3 times) |
| Minimum | 2 |
| Maximum | 9 |
| Range | 7 |
| Population standard deviation | 2 |
| Sample standard deviation | ≈ 2.13808994 |
Assumptions and limits
- Up to 2,000 numbers can be entered. Each can have up to 30 digits.
- The sum, mean, median and range are exact. A mean that does not end (such as 5 ÷ 3) is rounded to 6 decimals and marked with ≈, and standard deviations are rounded to 8 decimals because they involve a square root.
- The calculator treats each number equally. For a weighted average, repeat each value by its weight or use a weighted-average tool.
- An average hides the shape of the data: always look at the minimum, maximum and median alongside it.
Frequently asked questions
How do I calculate the average of a set of numbers?
Add all the numbers, then divide the total by how many numbers there are. The average of 12, 15 and 21 is 48 ÷ 3 = 16.
What is the difference between mean, median and mode?
The mean is the sum divided by the count. The median is the middle value of the sorted list. The mode is the most frequent value. For 1, 2, 2, 3, 12 the mean is 4, the median 2 and the mode 2; the large value 12 pulls the mean up but barely affects the median.
When should I use the median instead of the mean?
When the data has outliers or is skewed, such as salaries, house prices or response times. The median describes the typical value; the mean describes the arithmetic balance point.
What is the difference between population and sample standard deviation?
Both measure spread. The population formula divides by n and is used when the list is the entire group. The sample formula divides by n − 1 to correct for the bias of estimating the mean from the same data, and is the right choice when the list is a sample.
Can a set of numbers have more than one mode, or none?
Yes. If two values tie for most frequent, both are modes. If every value appears exactly once, there is no mode, and the calculator says so.
Why is my average shown with ≈?
The exact mean has more decimals than the six shown, for example 5 ÷ 3 = 1.666…. The ≈ tells you the figure was rounded; the sum is always exact.