Calculator guide
Statistics helps you explore the stated math question. Start with the labelled inputs, then review the method, worked example and limitations before using a result.
Formula or method
For N observations, mean = sum/N; median is the sorted middle observation or the average of the two middle observations. Population variance = sum((x−mean)²)/N, and population standard deviation is its square root. Range = maximum−minimum. Mode lists the most frequent values when a value repeats.
How to use this calculator
- Enter 1–1000 finite decimal observations separated by commas, spaces or semicolons. Invalid or empty entries reject the dataset.
- Read population variance and standard deviation using divisor N; do not interpret them as sample estimates.
Worked example
For 2, 4, and 6, count = 3, sum = 12, mean = median = 4, range = 4, population variance = 8/3, and population standard deviation ≈ 1.633. There is no mode.
Understanding the result
Compare the output with the statistics worked example using exactly the same inputs. A different assumption or rounding convention can produce a different displayed result; the output does not establish personal or professional suitability.
Limitations and assumptions
- Enter 1–1000 finite decimal observations separated by commas, spaces or semicolons, all in the same unit. Empty fields and invalid tokens reject the whole dataset. Nonzero magnitudes must be from 1e-150 to 1e150; precision failures are errors. This tool uses population divisor N, not sample divisor N−1. Small nonzero results use scientific notation.
- The worked example demonstrates the stated assumptions, not a recommendation about your personal circumstances.
Frequently asked questions
Which inputs should I check first?
Follow the Statistics input instructions above. Check each measurement, date, selection or expression before comparing results.
Why might my result differ from another tool?
Compare the other tool's statistics method, input units, rounding and assumptions. A matching title does not guarantee that both tools answer the same question.
Does a linked reference certify this result?
No. A reference can explain a formula or provide background for Statistics, but it does not endorse this website, validate personal inputs or establish professional suitability.
Sources
Educational and planning information only. Sources are attributed background or formula references, not endorsements. Verify consequential decisions with an appropriate qualified professional.