Average, median and mode calculator
Paste your list of numbers and get the mean, median, mode, range and standard deviation.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- Paste your list of numbers and get the mean, median, mode, range and standard deviation.
- Formula used
Mean: x̄ = Σxᵢ / n- Example
- Data: 8, 6.5, 9, 7, 10
Average calculator
You can paste numbers separated by commas, spaces or one per line — all three are recognised, so a column copied straight from a spreadsheet works.
Besides the mean it returns the median and the mode, which describe the data better when extreme values are present.
How it works
The mean adds every value and divides by how many there are. The median sorts the data and takes the middle value, or the average of the two middle values when the count is even.
The mode is the most repeated value; if nothing repeats there is no mode and a dash is shown.
Formula
Mean: x̄ = Σxᵢ / n
Median: middle value of the sorted data
Sample standard deviation: s = √( Σ(xᵢ − x̄)² / (n − 1) )
Worked example
Data: 8, 6.5, 9, 7, 10
1. Sum = 40.5
2. Mean = 40.5 ÷ 5 = 8.1
3. Sorted: 6.5 · 7 · 8 · 9 · 10 → median = 8
4. No value repeats: there is no mode
Explanation
The mean can be the worst possible summary
If ten people earn a thousand and one earns a million, the mean is about ninety thousand. None of the eleven earns anything like that figure. In distributions with extreme values, the median describes what is typical far better, which is why salary and house price data are almost always published as medians.
Mean, median and mode
The mean shares the total among everyone. The median is the middle value when you sort the data: half falls below it. The mode is the value that repeats most. All three are legitimate averages answering different questions.
Standard deviation completes the picture
Two sets can share a mean and behave in opposite ways. Marks of 5, 5 and 5 average 5, and so do marks of 0, 5 and 10. Standard deviation is what separates a homogeneous group from one where anything goes, and no mean should be published without it.
Sample or population
If your data are the whole population, divide by the number of values. If they are a sample of something larger, divide by one less, because a sample tends to underestimate real dispersion. With many data points the difference is minimal; with few, noticeable.
Frequently asked questions
Can I paste a column from Excel?
Yes. Copy the column and paste it directly: line breaks are treated as separators.
Which standard deviation is calculated?
The sample one, dividing by n−1. That is the right choice when your data is a sample of a larger population.
What if my values carry different weights?
Then you need a weighted average; use the weighted average calculator instead.
When should I use the median instead of the mean?
When extreme values distort the picture, as with salaries or house prices. The median better reflects the typical case.
Which standard deviation does this tool calculate?
Both. The population one if your data are the complete set, and the sample one if they are a sample of something larger.
Need to calculate something else?
These tools are often used alongside this calculator.
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