Mathematical Tools
What It Does
Computes descriptive statistics — count, sum, mean, median, mode, range, variance, standard deviation, quartiles, IQR, and outliers — for a set of numbers, with an optional histogram and box-plot. Everything runs in your browser.
How to Use It
- Paste or type your numbers, separated by commas, spaces, tabs, or newlines.
- Pick a quartile method and an outlier rule if the defaults don’t fit.
- Read the summary; toggle the histogram; adjust precision.
- Copy any statistic or export the summary as CSV/Excel.
Options Explained
| Option | Description |
|---|---|
| Quartile method | How Q1/Q3 are interpolated (methods legitimately differ for small samples). |
| Outlier rule | IQR × 1.5 (Tukey), IQR × 3 (far outliers), Z-score > 3, or none. |
| Precision | How many significant digits to show. |
| Thousands | Group large integer parts with separators. |
| Histogram / Bins | Show a frequency histogram; choose an automatic or fixed number of bins. |
Enter some numbers to see the statistics.
About Averages, Spread & Quartiles
“Average” can mean several things. The mean adds everything up and divides by the count; the median is the middle value once sorted; the mode is the most frequent value. They differ most when data is skewed — a few very large values pull the mean up while the median barely moves, which is why incomes are usually reported as a median.
Spread is captured by the variance and its square root, the standard deviation — and there’s a subtle but important distinction: divide the sum of squared deviations by n for a whole population, but by n − 1 for a sample (Bessel’s correction), because a sample slightly underestimates the true spread.
Quartiles split sorted data into four equal parts (Q1, median, Q3); the gap between Q1 and Q3 — the interquartile range — is a robust measure of spread that ignores extremes, and the classic Tukey rule flags anything more than 1.5 × IQR beyond the quartiles as an outlier. Different software computes quartiles with slightly different interpolation rules, so small samples can legitimately give different Q1/Q3 values — this tool lets you pick the method. Everything is computed on your device with numerically stable formulas.