The Statistics Calculator computes the count, sum, mean, median, mode, range, standard deviation, variance, quartiles and more from a list of numbers.
| Count | 8 |
| Sum | 178 |
| Mean (average) | 22.25 |
| Median | 23 |
| Mode | 23 (appears 3 times) |
| Largest | 38 |
| Smallest | 2 |
| Range | 36 |
| Sample standard deviation | 12.302729 |
| Population standard deviation | 11.508149 |
| Sample variance | 151.357143 |
| Geometric mean | 17.119852 |
| Quartiles (Q1, Q2, Q3) | 18.25, 23, 26.75 |
| Interquartile range | 8.5 |
| Sorted | 2, 10, 21, 23, 23, 23, 38, 38 |
Descriptive statistics summarise a data set in a few numbers: where its centre is (mean, median, mode), how spread out it is (range, variance, standard deviation, interquartile range) and its shape. They are the first step in any data analysis.
Mean = Σx ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1); population variance divides by n. Standard deviation is the square root of the variance. The geometric mean is the nth root of the product of n positive values.
Worked example (defaults): 10, 2, 38, 23, 38, 23, 21, 23. Sum 178, mean 22.25, median 23, mode 23 (three times), range 36, sample standard deviation about 12.3.
Quartiles split sorted data into four equal parts. The interquartile range (Q3 − Q1) covers the middle half. Values more than 1.5 × IQR below Q1 or above Q3 are often flagged as outliers.
Use the population formulas when you have every member of the group, and the sample formulas (dividing by n − 1) when your data is a sample used to estimate the population.
Mean or median? The median resists outliers; use it for skewed data like incomes.
Can a data set have several modes? Yes, or none if all values are unique.
How should I separate numbers? Commas, spaces or new lines all work.