Statistics Calculator
Paste in a list of numbers to get the full set of summary statistics: mean, median, mode, range and spread.
Formula
Mean = Σx ÷ n · Median = the middle value when sorted · Mode = the most frequent
- With an even count the median averages the two middle values
- Range = highest − lowest
For 2, 4, 4, 4, 5, 5, 7, 9: mean 5, median 4.5, mode 4, range 7
The Three Averages
- Mean: add everything and divide by the count
- Median: the middle value once sorted
- Mode: the most frequently occurring value
They answer different questions, and the gap between them is informative. UK household income has a mean well above its median, because a small number of very high earners pull the average up while leaving the midpoint where it is.
When to Prefer the Median
The mean is sensitive to outliers; the median is not. Adding a billionaire to a room of ten people changes the mean income dramatically and the median barely at all.
As a rule: use the median for skewed data such as income, house prices or response times, and the mean for roughly symmetric data. Reporting only the mean for skewed data is one of the most common ways statistics mislead without technically lying.
Spread Matters as Much as Centre
An average alone hides a great deal. Two data sets can share a mean of 50 while one runs from 49 to 51 and the other from 0 to 100.
Range (highest minus lowest) is the simplest measure of spread but is decided entirely by two extreme values. Standard deviation uses every point and is the more informative figure. Always quote a measure of spread alongside an average.
Quick Reference
| Measure | Value | What it tells you |
|---|---|---|
| Mean | 5.0 | The total shared equally |
| Median | 4.5 | The middle-ranked value |
| Mode | 4 | The most common value |
| Range | 7 | The spread from lowest to highest |
Frequently Asked Questions
- What is the difference between mean, median and mode?
- Mean is the arithmetic average, median the middle value when sorted, and mode the most frequent value. They coincide only in symmetric data.
- When should I use the median instead of the mean?
- When the data is skewed or contains outliers, such as income or house prices. The median is unaffected by extreme values.
- Can a data set have more than one mode?
- Yes. Two equally frequent values make it bimodal, and if no value repeats there is no mode at all.
- Why does spread matter?
- Because identical averages can describe very different data. Two sets averaging 50 might range from 49 to 51 or from 0 to 100.