Statistics Calculator
Summarize a numeric dataset in your browser. Review both population and sample measures of spread.
Mean = Σx/n. Population variance = Σ(x−x̄)²/n; sample variance = Σ(x−x̄)²/(n−1). Standard deviation is the square root of the corresponding variance. Sample measures, including SE, require n ≥ 2. SE = s/√n; CV = s/x̄; RSD = |CV| × 100%.
Results use floating-point arithmetic, rounded to 12 significant digits. CV and RSD are undefined when mean ≤ 0. CV is meaningful only on a ratio scale with a true zero and can be unstable near zero. All tied most frequent values are modes; if each value occurs once, there is no mode. No significance tests or causal conclusions are provided.
Definitions: NIST EDA Handbook and Dataplot: NIST EDA Handbook; NIST Dataplot
A QUICK WALKTHROUGH
How to use this tool
- Enter decimal numbers separated by commas, spaces or new lines.
- Calculate the statistics or sort the data.
- Review the results and the population and sample formulas.
Descriptive statistics
Mean = Σx/n. Population variance = Σ(x−x̄)²/n; sample variance = Σ(x−x̄)²/(n−1). Standard deviation is the square root of the corresponding variance. Sample measures, including SE, require n ≥ 2. SE = s/√n; CV = s/x̄; RSD = |CV| × 100%.
Numbers
Use a dot for decimals; scientific notation is accepted. Commas separate values, not thousands. Up to 50,000 characters and 10,000 values.
Descriptive statistics
Results use floating-point arithmetic, rounded to 12 significant digits. CV and RSD are undefined when mean ≤ 0. CV is meaningful only on a ratio scale with a true zero and can be unstable near zero. All tied most frequent values are modes; if each value occurs once, there is no mode. No significance tests or causal conclusions are provided.
GOOD TO KNOW
Common questions
When should I use population or sample measures?
Use population measures for the entire population of interest, and sample measures for a sample drawn from a larger population. These summaries alone do not establish representativeness.