The statistics calculator summarizes a numerical dataset with count, sum, mean, median, mode, range, variance, and standard deviation. You can choose sample or population deviation so the denominator matches your analysis.
How to use this calculator
Paste or type numbers separated by commas, spaces, semicolons, or new lines. Select sample deviation for data drawn from a larger population, or population deviation when the entered values represent the entire group of interest.
Formula & calculation method
Mean = Σx/n; sample variance = Σ(x−mean)²/(n−1); population variance = Σ(x−mean)²/nMedian is the middle sorted value or average of the two middle values. Modes are values tied for the highest frequency, reported only when at least one value repeats. Range is maximum minus minimum.
Worked example
For 2, 4, 4, 8, the mean is 4.5, the median is 4, and the mode is 4. Sample variance divides squared deviations by three, while population variance divides by four.
Why this is useful
One consistent summary reduces manual spreadsheet setup and makes the sample-versus-population choice explicit. Multiple central-tendency measures help reveal how distribution and repeated values affect interpretation.
Limitations to keep in mind
These descriptive statistics do not establish causation or represent data quality. Outliers can strongly affect mean and variance, and a small sample may be unstable. Invalid tokens are rejected rather than silently discarded.
Frequently asked questions
Which standard deviation should I choose?
Use sample deviation when generalizing from a sample to a larger population. Use population deviation when your list is the complete group being described.
What if every value occurs once?
There is no meaningful repeated mode, so the calculator reports no mode rather than listing every value.
Can there be more than one mode?
Yes. Values tied for the same highest repeated frequency are all reported as modes.