Mean, Median, Mode & Range Calculator
Paste up to 200 finite values to see the sorted list, count, sum, mean, median, every mode, range, and population or sample standard deviation.
Summarize a number list
Separate values with commas, spaces, semicolons, or line breaks. Negative values and decimals are allowed; words, blank tokens, and non-finite values are rejected.
Primary result
The 6 entered values have a mean of 8.3333333333, median of 8, mode of 7, and range of 9.
Read center and spread together
No single descriptive statistic tells the whole story. Mean uses every value and is useful for balancing a total across the count. Median identifies the middle of the ordered observations and is often steadier when an outlier is present. Mode identifies the most frequent value or values. Range shows the full endpoint spread but says nothing about how observations are distributed between those endpoints.
- Inputs: one to 200 finite numbers and an optional standard-deviation toggle.
- Outputs: sorted values, count, sum, mean, median, modes, range, population standard deviation, and sample standard deviation.
- Privacy: calculation runs locally in the page. Avoid placing confidential identifiers in the list; only numeric observations belong here.
Formula and methodology
The arithmetic mean equals the sum of all observations divided by the number of observations: x̄ = Σx ÷ n. The median is the middle sorted value when n is odd; when n is even, it is the mean of the two middle values. Mode comes from a frequency count. This implementation reports every value tied at the highest repeated frequency and reports “No mode” when no value occurs more often than the others.
Range equals maximum minus minimum. Population standard deviation is the square root of the mean squared distance from the arithmetic mean. Sample standard deviation uses the same squared deviations but divides by n − 1; it therefore needs at least two values. These are descriptive results, not a test of statistical significance or a claim that a sample represents a broader population.
Worked examples
Six-value example
For 4, 7, 7, 9, 10, and 13, the count is 6 and sum is 50. Mean is 50 ÷ 6 = 8.3333. The middle pair is 7 and 9, so median is 8. Seven occurs twice and every other value once, making 7 the mode. Range is 13 − 4 = 9.
An outlier changes some measures more than others
For 2, 3, 3, 4, and 100, mean is 22.4 while median and mode are both 3. The 100 also expands the range and standard deviations. The difference is not an error: each measure answers a different question about the same list.
A multimodal list
For 1, 1, 2, 2, and 3, both 1 and 2 occur twice. The calculator reports both modes rather than arbitrarily selecting one.
Common mistakes
- Treating the mean as a “typical” observation without checking skew or outliers.
- Using sample standard deviation for a complete population, or population standard deviation for a sample intended to estimate a broader population.
- Assuming every data set must have exactly one mode.
- Mixing observations measured in different units or time periods.
- Rounding each value before entering it instead of rounding only the final result.
FAQ
Does the calculator support negative values and decimals?
Yes. It accepts finite signed numbers including decimals and scientific notation understood by the browser number parser.
Why does a list sometimes have no mode?
If every distinct value has the same frequency, none is more common than the others. The page uses the convention “No mode” rather than listing the entire data set.
Which standard deviation should I use?
Use population standard deviation when the entered observations are the entire population you intend to describe. Use sample standard deviation when they are a sample and the n − 1 correction matches your analysis plan. Neither choice repairs biased sampling or poor measurements.
How this calculator helps
Use it to: Summarize a finite list with center, frequency, spread, and optional standard-deviation measures.
Inputs and example scenarios
These examples show how the result changes with different inputs. Change the values to match the decision you are making.
starting example: Include population and sample standard deviation: yes; Number list: 4, 7, 7, 9, 10, 13.
materially different higher mean, median, mode & range calculator scenario: Include population and sample standard deviation: yes; Number list: 2, 4, 4, 8, 10.
What changes the result
Outliers affect the mean, range, and standard deviations more strongly than the median; duplicate frequency determines the mode.
Formula and limitations
The calculator sorts the list, derives count and sum, calculates arithmetic mean and median, finds repeated modes, subtracts endpoints for range, and uses population or sample variance denominators for standard deviation. All results use declared descriptive-statistics identities and the visitor-entered list; no external observations are supplied.