How this calculator works
- Step 1Add the values80The example list is 10, 20, 20, 30.
- Step 2Count the entries4Repeated values still count as separate observations.
- Step 3Divide sum by count20This is the ordinary arithmetic mean.
The arithmetic mean spreads the sum equally over the observations. The median instead finds the centre after sorting, and the mode identifies values that repeat most often. These answers describe different things; they need not agree.
With an even count, the median averages the two central sorted values. With an odd count, it is the central value itself. This calculator reports all tied repeated-value modes, in ascending order.
Worked example: mean, median and mode
- Ordinary mean
mean = sum of values ÷ count- Weighted mean
weighted mean = sum(value × weight) ÷ sum(weights)
- List10, 20, 20, 30
- Sum80
- Number of observations4
- Sum divided by count20
- Middle of the sorted list20
- Most frequent repeated value20
The default mean, median and mode happen to coincide. That does not make them interchangeable. If every entry is unique, the tool says No repeated value rather than listing every number as a mode.
When weights change the answer
- Ordinary mean23.333333Each entered value counts once.
- Weighted mean22.5The middle value counts twice in this example.
- Unweighted median20Sorting ignores the optional weights.
Weights express how much each entry counts. For group averages, use group sizes: averaging two group means without their sizes can misrepresent the combined group. For coursework, use the official component weights only if the grading method is a weighted mean.
- Sum of value × weight90
- Sum of weights4
- Weighted sum divided by total weight22.5
Weights can be decimals and do not have to add up to one hundred. Scaling every weight equally leaves the weighted mean unchanged. A zero weight removes an entry only from the weighted calculation, not from ordinary statistics.
A large value can pull the mean
- Original list mean20Median: 20.
- Replace the last value with 15050Median: 20. The middle stayed put.
The mean reacts to the size of every observation. The median depends on sorted positions, so an extreme observation can shift the mean without shifting the median. Neither answer automatically makes an observation wrong; examine the data and its purpose.
Input conventions, limits and privacy
Use commas, semicolons, spaces or new lines between numbers. A dot marks the decimal point. Negative numbers and scientific notation are accepted. Empty comma-separated cells are errors, not silently missing observations.
You can enter up to one thousand values, each with absolute value up to one trillion. Optional weights need one entry per value, each from zero to one million, with at least one positive entry. Each text field is limited to twenty thousand characters.
Calculation uses floating-point numbers with compensated summation to reduce cancellation error. Display rounds to at most six decimals; very small and large answers use scientific notation. This is not exact decimal or arbitrary-precision arithmetic.
The list stays in the browser. The address stores it after the hash, not in a server query. Analytics receives neither the list nor its weights. Anyone receiving the full address can still read the list, so avoid sharing sensitive data.
Common average mistakes
Mistake: Write a thousands-grouping comma inside a number.
Instead: Write 1000 for one thousand; a comma creates a separate entry.
Mistake: Average group averages without checking group sizes.
Instead: Use group sizes as weights when reconstructing their combined mean.
Mistake: Assume weights also change median and mode.
Instead: Only the weighted mean uses weights here; other statistics stay unweighted.
Mistake: Compare a mean across unrelated units.
Instead: Convert to a common unit and confirm the numbers measure the same thing.
Related statistics tools
An average describes the centre of a list. Spread and position need other measures.
To measure how spread out the values are, use the standard deviation calculator. The percentile calculator shows where one value sits, and the grade calculator handles weighted course marks.
Checking the method
The mean, median and mode conventions follow NIST and OpenStax. Golden tests use rational sums, deviation balancing and expanded integer-weight lists. Tests also cover ties, negative values, malformed lists, cancellation and input limits. Sources and review details appear below.
Read how we test our calculators, or browse more maths calculators.