Free statistics calculator
Compute descriptive statistics from any dataset — enter your numbers to see mean, median, mode, variance, standard deviation, and quartiles, updated live, as you type.
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Population statistics. Source: standard descriptive statistics.
Results are estimates. Consult a professional.
How the statistics calculator works
This calculator computes the most common descriptive statistics for a data set in one step: mean, median, mode, variance, standard deviation, and interquartile range (IQR). Enter your numbers separated by commas and every metric is calculated simultaneously.
Worked example: eight-value data set
A teacher records eight quiz scores: 2, 4, 4, 4, 5, 5, 7, 9. She wants the mean, standard deviation, and spread in one calculation.
Descriptive statistics formulas at a glance
Use this table to quickly identify which statistic measures what aspect of your data set.
| Statistic | Formula | Measures |
|---|---|---|
| Mean | Σx ÷ n | Central tendency (average) |
| Median | Middle value(s) | Central tendency (robust to outliers) |
| Mode | Most frequent value | Most common value |
| Variance (pop.) | Σ(x−μ)² ÷ n | Average squared deviation |
| Std deviation | √variance | Spread in original units |
| IQR | Q3 − Q1 | Spread of the middle 50% |
| Range | Max − Min | Full spread of data |
Source: NIST/SEMATECH e-Handbook of Statistical Methods.
Tips for interpreting descriptive statistics
Descriptive statistics summarise your data, but choosing which measure to report depends on the shape of the distribution and the presence of outliers.
- Use the median for skewed data — incomes, house prices, and response times are right-skewed; the median resists the pull of extreme values better than the mean.
- Report IQR alongside median — together they describe the centre and spread without being distorted by outliers, making them the standard pair in box plots.
- Check mean vs. median — if they differ substantially, your data is skewed; investigate which direction and whether outliers are valid data points.
- Population vs. sample variance — divide by n for a full population; divide by n−1 (Bessel's correction) when your data is a sample drawn from a larger group.
- Mode is most useful for categorical data — for continuous numeric data, mode is often not meaningful unless several exact repeats appear.
Accuracy and limitations
All calculations use standard arithmetic with floating-point precision. For very large data sets or values with many decimal places, minor rounding differences may appear in the last digit. Population formulas (dividing by n) are used by default; for inferential work on a sample, note that sample standard deviation (dividing by n−1) gives an unbiased estimate of the population spread. This calculator does not perform hypothesis tests, regression, or inferential statistics.
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About this calculator
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