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Statistics tool

Descriptive Statistics Calculator

Summarize the center and spread of one ungrouped number list with each convention and boundary stated plainly.

Free · Private · Runs in your browser

Center and spread for one number list

Enter ungrouped numeric observations

Separate values with commas, semicolons, spaces, or new lines. Your list and results stay in your browser.

Up to 1,000 finite values; each value must be from −1,000,000,000,000 through 1,000,000,000,000.

Summary statistics will appear here after you submit a valid list.

Formulas and calculation method

The arithmetic mean is the sum of all observations divided by their count. The median is the middle sorted observation, or the mean of the two middle observations when the count is even. A mode is any value tied for the highest frequency, but this calculator reports “No mode” when every value occurs only once.

The range is maximum minus minimum. Population standard deviation divides the sum of squared differences from the mean by N before taking the square root. Sample standard deviation divides by n − 1 and is unavailable for a one-value list.

Summation uses compensated floating-point addition. Variance uses a two-pass calculation: the mean is calculated first, then squared differences are summed. These choices reduce, but do not eliminate, binary floating-point rounding error.

Conventions and boundaries

  • Data shape: one ungrouped list of finite numbers, separated by commas, semicolons, whitespace, or new lines.
  • Mode equality: values are equal after JavaScript numeric parsing. Negative zero is normalized to zero; near-equal values are not merged.
  • Standard deviation: both population (N) and sample (n − 1) results are shown so the denominator is never inferred silently.
  • Display precision: results display up to ten decimal places and omit unnecessary trailing zeroes. Internal calculations use JavaScript double-precision numbers.
  • Input bounds: lists may contain 1 through 1,000 observations. Each must be between −1,000,000,000,000 and 1,000,000,000,000.
  • Fixed versus changing values: all values are entered by the user. The calculation uses no live data, weights, forecasts, or external defaults.

Limitations

Summary measures do not show the full data distribution and do not establish representativeness, causation, significance, or data quality. Mean, range, and standard deviation can be sensitive to extreme observations. This tool does not calculate quartiles, percentiles, outliers, weighted or grouped data, confidence intervals, or inferential statistics. Review the raw data and its collection context before consequential use.

Worked example

For 2, 4, 4, 4, 5, 5, 7, and 9, the count is 8, sum is 40, mean is 5, median is 4.5, mode is 4, range is 7, population standard deviation is 2, and sample standard deviation is about 2.1380899353.

Common questions

Should I use population or sample deviation?

Use the population result when the entered values are the entire population you intend to describe. The sample result uses the n − 1 denominator commonly used when the values are treated as a sample. The calculator cannot decide which interpretation matches your study design.

Why can a data set have more than one mode?

Multiple values can share the highest frequency. This tool lists every tied mode in ascending order. If all frequencies are one, it reports no mode.

Why may the mean differ from the median?

The mean uses every numeric value and can move toward an extreme observation. The median depends on sorted position, so it can be less sensitive to an extreme value.

Use the Percentage Calculator for part-to-whole relationships, or the Compound Interest Calculator for repeated growth with transparent timing conventions.

Version and verification

Calculation version 1.0.0; formulas and deterministic fixtures last verified 2026-08-06. Authority pages were retrieved 2026-08-06. Automated tests cover formulas, input boundaries, metadata, privacy, keyboard use, responsive layout, contrast, and Axe behavior. Manual VoiceOver remains waived and is not claimed as passed.