Statistics Calculator
Get a full set of descriptive statistics from a list of numbers, including outliers.
Describing a data set
Descriptive statistics summarise a list of numbers: where its centre is (mean, median, mode), how spread out it is (range, quartiles, standard deviation) and what shape it has (skewness, outliers).
What you get
- Mean, median, mode for the centre.
- Q1, Q3 and the interquartile range (IQR) for the middle half of the data.
- Standard deviation and variance, both for a sample and for a whole population.
- Outliers, which are values more than 1.5 × IQR below Q1 or above Q3.
Example
With the starting values shown (Numbers 12, 15, 11, 18, 22, 14, 15, 30, 13, 16), Mean comes out as 16.6. Other results include median: 15; mode: 15; count: 10.
Example: ten numbers
For 12, 15, 11, 18, 22, 14, 15, 30, 13, 16 the calculator gives:
| Measure | Value |
|---|---|
| Mean | 16.6 |
| Median | 15 |
| Mode | 15 |
| Range | 19 (11 to 30) |
| Q1 and Q3 | 13 and 18 |
| Interquartile range | 5 |
| Sample standard deviation | 5.66 |
| Population standard deviation | 5.37 |
| Outliers | 30 |
Spotting outliers
The common rule flags any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. Here the limits are 13 − 7.5 = 5.5 and 18 + 7.5 = 25.5, so 30 is an outlier. It pulls the mean (16.6) above the median (15), which is why the median is the better measure for skewed data.
Which measure to use?
- Mean and standard deviation suit symmetrical data without outliers.
- Median and interquartile range suit skewed data or data with outliers.
- Skewness shows which way the data leans: positive means a long tail to the right.
Next steps: Mean, Median, Mode and Range Calculator, Standard Deviation Calculator, Z-Score Calculator.
Frequently asked questions
How do I find the quartiles?
Sort the data, split it at the median, and take the median of each half. Methods differ slightly between textbooks and software.
What is an outlier?
A value unusually far from the rest, often defined as more than 1.5 times the interquartile range beyond the quartiles.
What is the difference between sample and population standard deviation?
The sample version divides by n − 1 and is used when your data is a sample of a larger group.
What does skewness mean?
A measure of asymmetry. Zero means symmetric, positive means a longer right tail, and negative a longer left tail.
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