Statistics Calculator guide
Statistics Calculator: Mean, Median, Mode and Standard Deviation
Use our statistics calculator to find the mean, median, mode, range, quartiles, variance and standard deviation of your data, for a sample or a population.
By the AllCalculator editorial teamUpdated 15 October 20262 min read
Whether it's exam results, survey answers or lab readings, a few summary numbers tell you a lot about a set of data. Our Statistics Calculator works them all out from a list of numbers.
How to use the calculator (Statistics Calculator)
- Type or paste your numbers, separated by commas, spaces or new lines. You can paste a column straight from a spreadsheet.
- Choose whether your data is a sample or the whole population.
What each result means
- Mean: the average, the total divided by how many values there are.
- Median: the middle value when the data is in order. It isn't pulled around by extreme values.
- Mode: the most common value.
- Range: the largest value minus the smallest.
- Quartiles: the values a quarter (Q1) and three quarters (Q3) of the way through the ordered data. The interquartile range (Q3 − Q1) shows the spread of the middle half.
- Standard deviation: the typical distance of values from the mean. Bigger means more spread out.
- Standard error: how precisely the sample mean estimates the true mean.
Sample or population?
If your data includes every member of the group, choose population. If it's a sample from a bigger group, choose sample: the variance divides by n − 1 instead of n, which corrects for the sample underestimating the spread. Most real data is a sample.
A worked example
With the calculator's default data, 10 values from 12 to 35:
- Mean: 219 ÷ 10 = 21.9
- Median: halfway between 21 and 22 = 21.5
- Mode: 15 (it appears twice)
- Sample standard deviation: about 7.28
Planning a survey? Our Sample Size Calculator tells you how many responses you need.
Frequently asked questions
What's the difference between mean and median?
The mean is the average and can be pulled up or down by a few very large or small values. The median is the middle value, so it's better for skewed data like house prices or salaries.
Which standard deviation should I use?
Use the sample standard deviation unless your data covers the whole population.
How are quartiles worked out?
By linear interpolation between values, the same method as Excel's QUARTILE.INC. Other methods can give slightly different answers.
Summary statistics are the first step in understanding any data. Use the Statistics Calculator to get them in seconds.
Sources and further reading
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.