Find the mean, median, mode and range of a list.
Add the numbers and divide by how many there are. The average of 12, 15, 11, 18, 15, 20 is 15.1666666667.
Paste or type a list of numbers separated by commas, spaces or new lines and get the mean (average), median, mode, count, sum, minimum, maximum and range, plus the geometric and harmonic means for positive data and the sorted list. Averages summarise a data set with a single typical value.
For spread as well as centre use the Standard Deviation Calculator or the full Statistics Calculator. Grades can use the Grade Calculator; for arithmetic sequences see the Number Sequence Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Mean (average) | 15.1666666667 |
| Median (middle value) | 15 |
| Mode (most frequent) | 15 (appears 2 times) |
| Count | 6 |
| Sum | 91 |
| Minimum / maximum | 11 / 20 |
| Range | 9 |
| Geometric mean | 14.8425945798 |
| Harmonic mean | 14.5232273839 |
| Midrange | 15.5 |
| Position | Value |
|---|---|
| 1 | 11 |
| 2 | 12 |
| 3 | 15 |
| 4 | 15 |
| 5 | 18 |
| 6 | 20 |
| Data | Mean |
|---|---|
| 12, 15, 11, 18, 15, 20 | 15.1666666667 |
| 1, 2, 3, 4, 5 | 3 |
| 10, 20, 30, 40, 50 | 30 |
| 2, 4, 4, 4, 5, 5, 7, 9 | 5 |
| 100, 200, 300 | 200 |
Add them all up and divide by the number of values. 12 + 15 + 11 + 18 + 15 + 20 = 91; 91 ÷ 6 = 15.17.
Mean is the arithmetic average, median the middle value, and mode the most frequent value.
When the data has extreme values (outliers) — such as incomes — the median is less affected.
The nth root of the product of n positive numbers — used for growth rates and ratios.
If every value appears once, there is no mode; if several values tie, the data is multimodal.
The difference between the largest and smallest values — a simple measure of spread.
It uses the standard method: mean = Σx ÷ n geometric = (Πx)^(1/n) harmonic = n ÷ Σ(1/x) 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.
