Mean, median, mode and range calculator
Free TutorAura tool · no sign-up · Updated
Paste or type a list of numbers to find the mean, median, mode and range at once. The calculator puts the data in order and shows exactly how each value is worked out, which is what you need to show in an exam answer.
The four measures
| Measure | What it is | How to find it |
|---|---|---|
| Mean | The average when the total is shared equally | Add all the values, divide by how many there are |
| Median | The middle value | Put the values in order and find the middle one |
| Mode | The most common value | The value that appears most often (there can be more than one, or none) |
| Range | How spread out the data is | Largest value minus smallest value |
Worked example
Data: 4, 8, 6, 5, 3, 8, 9.
- In order: 3, 4, 5, 6, 8, 8, 9 (7 values).
- Mean: .
- Median: the 4th value of 7: 6.
- Mode: 8 (it appears twice).
- Range: .
With an even number of values, the median is halfway between the two middle values: for 1, 2, 3, 4 it's .
Which average should you use?
- Mean: uses every value, but extreme values (outliers) pull it a long way.
- Median: not affected by outliers, so it's often better for things like incomes or house prices.
- Mode: the only average for non-numerical data (favourite colour) and useful for "most common size".
Exam questions often ask you to compare two sets of data using an average and the range, and to say what each tells you in context. See mean, median, mode and range explained.
Common mistakes
- Finding the median without ordering the data first.
- Giving the position instead of the value: "the 4th value" isn't the median; the value in that position is.
- Saying the mode is the frequency: if 8 appears twice, the mode is 8, not 2.
- Range as a pair: the range is one number (largest − smallest), not "3 to 9".
Comparing two data sets
Exam questions often ask you to compare two groups. Make one comparison of an average and one of spread, and say what each means in context: "Group A had a higher median (14 vs 11), so they generally scored higher; Group B had a smaller range (6 vs 10), so their scores were more consistent." Run each data set through the calculator, then compare. More in mean, median, mode and range.
Frequently asked questions
What is the difference between mean and average?
In everyday language 'average' usually means the mean. In maths, mean, median and mode are all types of average, so exam questions say which one they want.
What if there are two modes?
The data is bimodal and both values are modes. The calculator lists all of them. If every value appears once, there is no mode.
How do I find the median of an even number of values?
Put them in order and take the mean of the two middle values.
Can I paste data from a spreadsheet?
Yes. Numbers separated by commas, spaces or new lines all work, up to 1,000 values.
Sources
- National curriculum in England: mathematics programmes of study. Department for Education.
- Common Core State Standards for Mathematics. Common Core State Standards Initiative.
Keep reading
Mean, median, mode and range explained (with examples)
How to find each measure, which average to use, and how to compare data sets in exam answers.
Averages and spread
Calculate and compare mean, median, mode and range, and reason about how data changes affect them.
An AI statistics tutor for school: data, graphs and probability
Averages, spread, graphs, probability and sampling for grades 6 to 12, with worked examples and practice.
Test grade calculator: score to percentage and letter grade
A test score as a percentage and letter grade, plus a table for every number of points lost.