Statistics Calculator
Mean, median, mode, standard deviation, quartiles, and outliers — from any list of numbers.
Mean
15.75
Median
14
Std dev
5.848
Range
22
31
Values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR. Worth a look, not automatic removal.
How to Use
- 1. Paste or type your numbers, separated by commas, spaces, or newlines.
- 2. Results update instantly as you type.
- 3. Choose how many decimal places to display.
- 4. Copy the full summary or review the distribution histogram.
Reading Your Results
The mean and median answer the same question differently. The mean uses every value, which makes it sensitive to extremes; the median is simply the middle value and barely moves when one number is far from the rest. When the two diverge sharply, your data is skewed — and the median is usually the more honest summary.
Standard deviation describes spread in the same units as your data. A small value means observations cluster near the mean; a large one means they scatter. The sample version divides by n−1 rather than n, which corrects for the fact that a sample's own mean sits closer to its data than the true population mean would — use it unless you genuinely measured every member of the group.
Quartiles split the sorted data into four parts, and the interquartile range (Q3 − Q1) captures the middle half. Because it ignores the tails entirely, IQR is a robust measure of spread and forms the basis of the outlier rule used here.
Related: Average Calculator, Percentage Calculator, and Scientific Calculator.
Frequently Asked Questions
What is the difference between sample and population standard deviation?
Population treats your numbers as the entire group and divides by n. Sample treats them as a subset drawn from a larger group and divides by n−1, which corrects for the fact that a sample tends to understate the true spread. Use sample unless you genuinely have every member of the group.
How are quartiles calculated?
By linear interpolation between the two nearest ranked values — the same method spreadsheets use, so Q1, the median, and Q3 match Excel and Google Sheets.
How are outliers identified?
Using Tukey's rule: any value more than 1.5 × IQR below Q1 or above Q3. It is a convention rather than a law — flag them for a closer look, not for automatic deletion.
What if my data has no mode?
When every value appears exactly once there is no meaningful mode, so none is reported. If several values tie for the highest frequency, all of them are listed.
What separators can I use?
Commas, spaces, tabs, semicolons, and newlines all work, so you can paste a spreadsheet column straight in. Anything that is not a number is counted and reported rather than silently dropped.
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