Maths
Average Calculator
Find the mean, median, mode, range and standard deviation of any list of numbers.
Updated 3 Sep 2026
Across 7 values the mean is 16.5714 and the median is 15. The values range from 4 to 42, with a population standard deviation of 11.9266.
Paste or type your numbers separated by commas, spaces or new lines. The calculator returns the mean, median, mode, sum, count, minimum, maximum, range and population standard deviation.
What is the Average Calculator?
"Average" usually means the arithmetic mean, but median and mode are also averages, and they answer different questions. Quoting the wrong one is a common way to mislead — accidentally or otherwise.
How to use the Average Calculator
- Enter your numbers, separated by commas, spaces or line breaks. Pasting a column from a spreadsheet works.
Non-numeric entries are ignored rather than causing an error.
Formula
Median = the middle value once sorted
(or the mean of the two middle values)
Mode = the most frequently occurring value
Range = maximum − minimum
Population standard deviation:
σ = √( Σ(x − mean)² ÷ n )
This uses the population standard deviation, dividing by n. If your numbers are a sample drawn from a larger group and you want to estimate that group's spread, the sample standard deviation divides by n − 1 instead and gives a slightly larger figure.
How the calculation works
The mean is a single balancing point but is pulled around by extreme values. The median is the middle of the sorted list and is unaffected by how extreme the outliers are. When the two differ substantially, the distribution is skewed.
Standard deviation measures typical distance from the mean — a small value means the numbers cluster tightly.
Worked example
For 4, 8, 15, 16, 23, 42, 8:
- Sum = 116, count = 7
- Mean = 116 ÷ 7 = 16.57
- Sorted: 4, 8, 8, 15, 16, 23, 42 → median = 15
- Mode = 8 (it appears twice)
- Range = 42 − 4 = 38
- Standard deviation ≈ 11.93
The mean sits above the median because 42 pulls it upward.
Uses and benefits
- Summarise a set of scores, prices or measurements at a glance.
- Spot skew by comparing mean against median.
- Check homework or a spreadsheet formula.
Frequently asked questions
The mean is the total divided by the count. The median is the middle value when sorted. The mode is the most frequent value. For income data the median is usually more representative, because a few very high earners pull the mean upward.
The population standard deviation, dividing by n. If your data is a sample and you want to estimate the wider population, use the sample version which divides by n − 1 and gives a slightly larger result.
Then there is no mode, and the calculator says so rather than reporting a misleading figure.