Statistics Calculator
Enter a list of numbers to calculate mean, median, modes, quartiles, population and sample standard deviation, with a frequency histogram.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sort the observations for medians and quartiles. Calculate the mean as sum divided by count. Population variance divides the sum of squared deviations by n; sample variance uses n − 1. The square root of variance is standard deviation.
mean = Σx/n; population variance = Σ(x − mean)²/n; sample variance = Σ(x − mean)²/(n − 1)
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: count = 8, mean = 5, median = 4.5, mode = 4, population variance = 4, and population standard deviation = 2.
Assumptions and input details
Commas separate observations; do not use commas as thousands separators. Quartiles use medians of the lower and upper halves, excluding the central observation for an odd-sized list. One observation has no sample variance. Up to 1,000 values are supported.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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