A complete summary of any data set in one click.
Paste your numbers to see the centre, spread, quartiles and outliers at once. The data 4, 8, 15, 16, 23, 42 has a mean of 18 and a median of 15.5.
This statistics calculator summarises a list of numbers with over twenty measures: count, sum, mean, median, mode, range, quartiles Q1 and Q3, the interquartile range, outlier fences and any outliers (1.5 × IQR rule), sample and population standard deviation, variance, standard error, mean absolute deviation, skewness, excess kurtosis and root mean square, plus a frequency table.
Use the dedicated Average Calculator and Standard Deviation Calculator for focused work, then go on to the Confidence Interval Calculator or Z-Score Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Count | 6 |
| Sum | 108 |
| Mean | 18 |
| Median | 15.5 |
| Mode | none |
| Minimum / maximum | 4 / 42 |
| Range | 38 |
| First quartile Q1 | 8 |
| Third quartile Q3 | 23 |
| Interquartile range (IQR) | 15 |
| Outlier fences (1.5 × IQR) | -14.5 and 45.5 |
| Outliers | none |
| Sample standard deviation | 13.4907375632 |
| Population standard deviation | 12.3153021346 |
| Sample variance | 182 |
| Standard error of the mean | 5.50757054729 |
| Mean absolute deviation | 9.66666666667 |
| Skewness (population) | 0.90747462 |
| Excess kurtosis (population) | -0.24008695 |
| Root mean square | 21.8097837373 |
| Value | Frequency | Relative frequency |
|---|---|---|
| 4 | 1 | 0.166667 |
| 8 | 1 | 0.166667 |
| 15 | 1 | 0.166667 |
| 16 | 1 | 0.166667 |
| 23 | 1 | 0.166667 |
| 42 | 1 | 0.166667 |
| Data | Mean |
|---|---|
| 4, 8, 15, 16, 23, 42 | 18 |
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 100 | 14.5 |
| 10, 20, 30, 40, 50 | 30 |
| 3, 3, 4, 5, 5, 5, 9 | 4.85714285714 |
| 2, 4, 6, 8, 10, 12 | 7 |
It computes summary measures that describe the centre, spread and shape of a data set.
The spread of the middle half of the data: Q3 − Q1. It is resistant to outliers.
Values more than 1.5 × IQR below Q1 or above Q3 are flagged as outliers.
A measure of asymmetry: positive skew has a long right tail, negative skew a long left tail, and zero means symmetric.
A measure of how heavy the tails are compared with a normal distribution (excess kurtosis 0).
Statistical software uses several conventions. This calculator uses the median-of-halves method taught in most textbooks.
It uses the standard method: IQR = Q3 − Q1 fences = Q1 − 1.5·IQR, Q3 + 1.5·IQR The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
