Average Calculator
Paste a list once to see its average, middle, most common value, and spread — with the sample or population choice visible.
- Fewer clicks, keyboard friendly
- Features others lock behind paywalls
Results
Mean = sum ÷ n · sample variance = Σ(x − mean)² ÷ (n − 1)
Your numbers are calculated in this browser and are never sent to a server.
How to use
- Paste or type numbers in the input box, separating values with commas, spaces, semicolons, or line breaks.
- Choose Sample (n − 1) for observations drawn from a larger group, or Population (n) for the entire group.
- Read the mean, median, mode, standard deviation, and the supporting summary statistics as they update.
- Use Copy results to put the main figures into a report or spreadsheet.
Mean, median, and mode answer different questions
The arithmetic mean is the sum of all values divided by their count: mean = Σx ÷ n. It is useful when every observation has equal weight, but a single extreme value can pull it away from what is typical. The median is the middle value after sorting; for an even count, it is the average of the two middle values. The mode is the value or values occurring most often. For 1, 2, 2, 9, the mean is 3.5 while both the median and mode are 2. Looking at all three prevents an unusually high or low observation from being hidden behind one average.
Choose sample or population standard deviation deliberately
Standard deviation measures typical distance from the mean. Use population standard deviation when the list is every member of the group you care about; its variance divides by n. Use sample standard deviation when the list is a sample intended to represent a larger population; its variance divides by n − 1. That n − 1 adjustment, often called Bessel’s correction, makes the sample estimate less systematically small. A one-value sample has no sample standard deviation because n − 1 is zero, while its population standard deviation is 0.
Pasting data and reading the other results
This calculator accepts decimal numbers, negative values, and scientific notation such as 1e3. A column copied from a spreadsheet can be pasted directly because line breaks and tabs are separators. The range is maximum minus minimum, and variance is the square of standard deviation, so variance is expressed in squared units. Zero is a valid value and is included in the count. Text, emoji, Infinity, and malformed numbers are identified and left out rather than silently being treated as zero; check the notice before using the result.
Frequently asked questions
How do you calculate an average?
An arithmetic average, also called the mean, is calculated by adding every value and dividing by the number of values: mean = Σx ÷ n. For 72, 85, and 90, the sum is 247 and the average is 247 ÷ 3 = 82.3333.
What is the difference between sample and population standard deviation?
Population standard deviation divides the squared distances from the mean by n because it describes the full group. Sample standard deviation divides by n − 1 because it estimates a larger group from a sample, so it is usually slightly larger for the same list.
Can a list have more than one mode?
Yes. A list can have multiple modes when several values tie for the highest frequency. For 1, 2, 2, 3, 3, 9, both 2 and 3 are modes; if every value occurs once, there is no mode.
Does this average calculator include zero?
Yes. Zero is a numeric observation, so it is included in the count, sum, mean, median, and standard deviation. Empty separators are ignored, but a typed 0 is never treated as an empty value.
Are my numbers uploaded anywhere?
No. The parsing and calculation run in JavaScript in your browser. The input is saved only in this browser so it can remain after a refresh; it is not sent to a server.
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Updated 2026-10-29