WIN-J NUMBER TOOLS
Mean, median and standard deviation calculator
Calculate sum, mean, median, modes, range and population or sample standard deviation from a list of numbers. Copy or save the summary.
Results
Standard deviations use divisors n for population and n−1 for sample. One value has population deviation 0 and no defined sample deviation. If no value repeats, no mode is reported.
How to use
- Paste numbers separated by commas, spaces or line breaks.
- Use a dot for decimals and omit thousands separators. Scientific notation such as 1e3 is accepted.
- Calculate and distinguish the population standard deviation for the whole data set from the sample standard deviation for a sample.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: mean 5, median 4.5, mode 4 and population standard deviation 2.
Method and limits
Up to 10,000 values and 100,000 input characters are supported. Values must be 0 or finite with magnitude 1e-100–1e100. Compensated summation and shifted Welford calculations reduce numerical error, but floating-point limits remain. Commas separate values.
Questions and answers
What if multiple values are modes?
All values tied for the highest frequency are shown in ascending order. A frequency of 1 is reported as no mode.
Does this handle weighted means or missing data?
All observations have equal weight. Empty separators are ignored, but text or NA is rejected instead of silently removed.