📊 Statistics Calculator
Paste your numbers, get the full descriptive-statistics table: mean, median, mode, quartiles, IQR, and both flavors of variance and standard deviation — with the sample/population distinction made explicit.
| Count (n) | 9 |
|---|---|
| Sum | 131 |
| Mean (average) | 14.555556 |
| Geometric mean | 14.114225 |
| Harmonic mean | 13.682132 |
| Median | 15 |
| Mode | 15 |
| Minimum · Maximum | 9 · 22 |
| Range | 13 |
| Q1 · Q3 (quartiles) | 11.5 · 16.5 |
| IQR (interquartile range) | 5 |
| Variance (population, σ²) | 13.135802 |
| Std. deviation (population, σ) | 3.6243348 |
| Variance (sample, s²) | 14.777778 |
| Std. deviation (sample, s) | 3.8441875 |
Z-score of a value — how many standard deviations from the mean?
Quartiles use the median-of-halves method (Moore & McCabe). Sample statistics divide by n−1 (Bessel's correction) — use them when your data is a sample of a larger population; population statistics divide by n. Computed locally.
How the statistics calculator works
Paste or type any list of numbers (commas, spaces or line breaks all work) and every descriptive statistic updates live: count, sum, mean, median, mode(s), min/max and range, the quartiles Q1 and Q3 with the interquartile range, and variance and standard deviation in both conventions — population (dividing by n) and sample (dividing by n−1, Bessel's correction). Quartiles use the median-of-halves method (Moore & McCabe), stated on the page because different textbooks define quartiles slightly differently and the method changes the answer.
The sample-vs-population distinction is the most common statistics mistake outside classrooms: divide by n when your data IS the whole population (all 30 students in the class), by n−1 when it's a sample standing in for something bigger (30 customers out of thousands). Excel's STDEV defaults to the sample version; many calculators default to population — knowing which you're getting is half the battle, so this tool always shows both, labeled.
Frequently asked questions
What's the difference between sample and population standard deviation?
Population σ divides the squared deviations by n; sample s divides by n−1 (Bessel's correction), which compensates for a sample underestimating spread. Use sample statistics when your data is a subset standing in for a larger population.
How are the quartiles computed?
Median-of-halves (Moore & McCabe): split the sorted data at the median (excluding it when n is odd); Q1 is the median of the lower half, Q3 of the upper. Other textbooks interpolate differently — check which your course uses.
What if there's no mode?
If every value occurs once, there is no mode and the tool says so. If several values tie for the highest frequency, all of them are listed (multimodal data).
What is the IQR used for?
The interquartile range (Q3 − Q1) is the spread of the middle 50% — robust to outliers, and the basis of the common outlier rule: flag values beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.
Is my data uploaded?
No — everything computes in your browser and works offline, which matters when the numbers are grades, salaries or measurements you'd rather keep local.