Statistics Calculator

Statistics calculator: every descriptive statistic from one paste

This statistics calculator takes a list of numbers in any format — copied from a spreadsheet column, typed with commas, or pasted one per line — and returns the complete descriptive summary: count, sum, mean, median, mode, minimum, maximum, range, sample and population variance and standard deviation, standard error, coefficient of variation, quartiles, interquartile range, outliers by the 1.5 × IQR rule, skewness, kurtosis, mean and median absolute deviation, and geometric and harmonic means.

Because quartiles are defined differently by different textbooks and programs, you can choose the method: linear interpolation (R type 7 and Excel QUARTILE.INC, the default), the Minitab/SPSS/QUARTILE.EXC method (type 6), or the median-of-halves rule used by TI-83 calculators. A histogram with automatic class widths and a box-and-whisker plot are drawn as SVG, and a frequency table lists each value or class with its percentage and cumulative percentage.

The data stay in your browser. The statistics table can be copied as tab-separated text straight into a report or spreadsheet.

How to use the Statistics Calculator

1. Paste or type your numbers into the data box. Spaces, commas, semicolons, tabs and new lines all work as separators; anything that is not a number is ignored and listed in a warning.
2. Choose a quartile method if your course or software uses a specific one. The default is linear interpolation (type 7).
3. Read the headline figures (mean, median, mode, sample SD, count) and the full table grouped into centre, spread, quartiles and shape.
4. Look at the histogram and box plot; hover a bar, the box or an outlier dot to see its value.
5. Open the frequency table for per-value counts, or press Copy table to export the statistics.

Statistics Calculator features

Worked example: 2, 4, 4, 4, 5, 5, 7, 9

Eight values sum to 40, so the mean is 5. Sorted, the two middle values are 4 and 5, so the median is 4.5, and 4 appears three times, so it is the mode. The squared deviations from the mean are 9, 1, 1, 1, 0, 0, 4 and 16, totalling 32: the population variance is 32 ÷ 8 = 4 (σ = 2) and the sample variance is 32 ÷ 7 = 4.571 (s = 2.138). With type 7 quartiles Q1 = 4 and Q3 = 5.5, so the IQR is 1.5 and the fences are 1.75 and 7.75 — the 9 lies above the upper fence and is flagged as a mild outlier. The sample skewness G1 is 0.82 (a right tail, pulled by that 9) and the excess kurtosis G2 is 0.94.

Why quartiles differ between calculators

There is no single definition of the 25th percentile for a finite sample. The type 7 method places Q1 at position (n − 1) × 0.25 + 1 in the sorted list and interpolates; type 6 uses (n + 1) × 0.25; the TI-83 method takes the median of the lower half of the data (excluding the overall median when n is odd). For the example above these give Q3 = 5.5, 6.5 and 6 respectively. All are legitimate — just use the one your course or software expects, and say which you used when you report IQR or outliers.

Reading skewness and kurtosis

When you need the next step, the z score calculator converts a value into standard deviations from the mean and the t test calculator compares two samples. The simpler standard deviation calculator shows the step-by-step deviation table.

• Skewness near 0 means a symmetric distribution; positive values indicate a longer right tail (incomes, waiting times), negative a longer left tail. Values beyond ±1 are usually called strongly skewed.
• Excess kurtosis compares tail weight with the normal distribution, which has 0. Positive values mean heavier tails and more outliers; negative values mean a flatter, lighter-tailed shape.
• Sample vs population versions: G1 and G2 include small-sample corrections and are what Excel, SPSS and most textbooks report; g1 and g2 are the plain moment ratios.
• MAD (median absolute deviation) is a robust spread measure: multiply by 1.4826 to estimate σ for roughly normal data without outliers dragging it.