Statistics Calculator
Paste a list of numbers to get the full descriptive summary — mean, median, mode, range, variance, standard deviation, quartiles and more.
How it works
The mean, median and mode describe the centre in different ways, and the difference between them is informative. When the mean sits well above the median, a few large values are pulling it — which is exactly when the median is the more honest summary.
Standard deviation comes in two forms and picking the wrong one is the classic error. Divide by n − 1 when your numbers are a sample from a larger population — the usual case, and what spreadsheets call STDEV. Divide by n only when you have the entire population.
The formula
Mean
x̄ = Σx ÷ n
Sample variance
s² = Σ(x − x̄)² ÷ (n − 1)
Population variance
σ² = Σ(x − x̄)² ÷ n
Interquartile range
IQR = Q3 − Q1
Worked examples
| Scenario | Working | Result |
|---|---|---|
| 12, 15, 15, 18, 21 | Sum 81 ÷ 5 | Mean 16.2, median 15, mode 15 |
| A set with one huge outlier | Mean pulled upward | Median is the better centre |
| Sample vs population SD on 12 values | n − 1 vs n | The sample figure is slightly larger |
When you'd use it
- Summarising an experiment's results for a lab report
- Checking coursework answers by hand
- Finding outliers using the interquartile range
- Comparing the spread of two data sets
Common questions
Should I use the sample or population standard deviation?
Sample, in almost every real case — your numbers are usually a sample drawn from something larger. Use the population figure only when the data covers every member of the group you care about.
What if there is no mode?
When every value appears once there is no mode, and the tool says so rather than inventing one. When several values tie for the highest frequency, all of them are listed.
How are the quartiles calculated?
By linear interpolation between the surrounding values, which is the method spreadsheets use. Some textbooks use a different convention, so a small difference from a printed answer key is expected rather than an error.
Are my grades sent anywhere?
No. Everything is calculated in your browser, so nothing you type is uploaded, logged or stored. There is no account and no record of what you entered.