Average calculator
Explore mean, median, modes, range, and standard deviation with a live distribution of your number list.
How it works & useful details
How it works & limits
Supports 1–1,000 values, up to 25,000 characters, and magnitudes up to 1e12. Thousands separators are not supported: 1,000 is two values, 1 and 0. Scientific notation such as 1e3 is accepted.
Mean is sum ÷ count. Median is the middle sorted value (or mean of the middle pair). Every repeated value tied for greatest frequency is a mode. Population deviation divides by n; sample deviation divides by n − 1. Floating-point results are rounded to 12 significant digits.
Your working space
Change the values to explore the preview. Use the action below to create a copyable, downloadable result. All calculations stay on this device; refreshing clears your work.
About this tool
Average calculator summarizes a list of numbers with the mean, median, modes, range, and standard deviation, plus a distribution view of the values. It is the fastest way to understand a dataset before doing anything more formal.
All statistics are computed locally from the numbers you paste, and the distribution chart updates live as you edit the list.
How to use it
- Paste or type your numbers, one per line or separated by commas.
- Read the mean, median, and mode results.
- Check the range and standard deviation for spread.
- Use the distribution view to spot clusters and outliers.
Worked example
For the list 12, 15, 18, 18, 22, 25, 30:
- Count 7, sum 140, so the mean is 140 ÷ 7 = 20.
- Sorted, the middle (fourth) value is 18, so the median is 18.
- 18 appears twice and every other value once, so the mode is 18.
- Range: 30 − 12 = 18.
- Population standard deviation 5.682; sample standard deviation 6.137.
Here the mean sits above the median because the larger values (25 and 30) are further from the centre than the smaller ones. That gap is a quick sign of a skewed list.
Mean, median, or mode?
The mean uses every value, so a single outlier moves it. Add 300 to the list above and the mean jumps from 20 to 55, while the median only moves from 18 to 20. Use the median for incomes, house prices, response times, and anything else with a long tail. Use the mean when every unit counts equally, such as total cost divided by items. The mode is most useful for repeated categories or ratings, and a list can have several modes.
Choose the population deviation when the list is the complete group you care about. Choose the sample deviation, which divides by n − 1, when the numbers are a sample drawn from a larger group. The sample version is slightly larger to compensate for the fact that a sample tends to underestimate spread.
Frequently asked questions
What happens when a list has several modes?
All values that occur most often are reported, so multimodal lists show more than one mode.
Which standard deviation is used?
The sample standard deviation, which is the usual choice when the list is a sample rather than an entire population.
What is the input limit?
Up to 25,000 characters of numbers per run.
How should I separate the numbers?
Use commas, spaces, or new lines. Do not use thousands separators: 1,000 is read as two values, 1 and 0. Write 1000 instead.