Standard deviation
Calculate sample and population variance and standard deviation together. See the mean, squared-deviation sum and the n versus n−1 denominator.
Mean, median, mode and range calculator
Summarize a list of numbers and inspect the ordered values behind the result. This tool reports all values tied for the highest repeated frequency; if every value appears once, it reports no repeated mode.
Free to use, with no sign-in. Inputs and results stay in this page and are not sent with the form. Download a result before leaving; this tool does not save your work.
Worked result
Mean 5; median 4; mode 4; range 7.
- Add the five values to get 25.
- Divide by five to get a mean of 5.
- The third ordered value is the median, and 4 is the most frequent value.
Summarize 2, 4, 4, 6 and 9
These five illustrative observations have one repeated value and an odd-sized ordered list.
Sum = 2 + 4 + 4 + 6 + 9 = 25
Mean = 25/5 = 5
Ordered values = 2, 4, 4, 6, 9
Median = 4
Mode = 4 (twice)
Range = 9 − 2 = 7Replacing 9 with 90 raises the mean to 21.2 but leaves the median at 4. That difference illustrates why one statistic rarely describes the whole distribution.
Location and spread answer different questions
The arithmetic mean gives each observation equal weight. The median uses order, with the two middle values averaged when the number of observations is even. A mode uses frequency rather than magnitude or position.
The range uses only the two extremes. It is useful for a quick check, but does not describe how the observations are distributed between them. Keep the sorted list, sample size and units alongside a numerical summary.
mean = sum(values)/n
median = middle value, or average of the two middle values
mode = value(s) with the highest repeated count
range = maximum − minimumInput limits and common mistakes
Enter 1–5,000 finite numbers with absolute value at most 1e100. Commas, semicolons and whitespace separate entries. Thus 1,000 is interpreted as two entries, 1 and 000; enter 1000 for one thousand.
Repeated modes use exact equality of parsed numbers, not bins or a smoothed distribution estimate. Results use floating-point arithmetic. This descriptive summary does not measure sampling bias or establish a population parameter.
Questions about mean, median and mode
Can there be more than one mode?
Yes. In 1, 1, 2, 2, 3, both 1 and 2 occur twice, so both are reported.
What if every number is different?
This tool reports “no repeated mode.” Some conventions call all equally frequent values modes; the convention is explicit here.
Why do the mean and median differ?
The mean responds to every numeric magnitude, while the median depends on position after sorting. Outliers can move the mean much more.
Sources and verification
These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.
- NIST: measures of location — Definitions and differing interpretations of mean, median and mode.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
Related tools
Weighted average
Calculate a weighted mean from value–weight pairs. See total weight, each weighted contribution and how percentage weights are normalized.
Percentage calculator
Calculate a percent of a number, express one number as a percent of another, or find the whole from a known part and percentage.
Further reading
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