Average Calculator
Find the mean, median, mode, sum and range of up to 10 numbers, with the work shown and a deviation table that explains what the mean really is.
Average Calculator: with the default inputs, mean (average) is 13.2.
Only the first N value boxes are used. Values 6–10 live under More options.
- Median (middle value)
- 15
- Mode (most frequent)
- None (each value appears once)
- Sum
- 66
- Smallest
- 4
- Largest
- 23
- Range (largest − smallest)
- 19
Assumptions
- All values are weighted equally (a simple, not weighted, average).
- When every value is equally common the set is reported as having no mode.
| Value | Value − mean |
|---|---|
| 4 | -9.2 |
| 8 | -5.2 |
| 15 | 1.8 |
| 16 | 2.8 |
| 23 | 9.8 |
The deviations always add up to zero — that's what makes the mean the balance point of the data.
How this is worked out
The formula
Mean = (x₁ + x₂ + … + xₙ) ÷ n Median = middle value of the sorted list (average of the two middle values when n is even) Mode = the value(s) that occur most often Range = largest − smallest
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- How many values?
- Only the first N value boxes are used. Values 6–10 live under More options.from 2 to 10 · whole numbers only · defaults to 5
- Value 1
- A number.defaults to 4
- Value 2
- A number.defaults to 8
- Value 3
- A number.defaults to 15
- Value 4
- A number.defaults to 16
- Value 5
- A number.defaults to 23
- Value 6(under More options)
- A number.defaults to 0
- Value 7(under More options)
- A number.defaults to 0
- Value 8(under More options)
- A number.defaults to 0
- Value 9(under More options)
- A number.defaults to 0
- Value 10(under More options)
- A number.defaults to 0
What you get back
- Mean (average)main answer
- Median (middle value)
- Mode (most frequent)
- Sum
- Smallest
- Largest
- Range (largest − smallest)
What this assumes
- All values are weighted equally (a simple, not weighted, average).
- When every value is equally common the set is reported as having no mode.
About this calculator
"Average" usually means the mean: add everything up and divide by how many there are. But the mean is only one of three ways to describe the "typical" value in a set, and this calculator gives you all of them so you can pick the one that tells the truth about your data.
How to use it
Set how many values you have (2–10), then type them in. Values 6 through 10 are under More options. Everything updates as you type, and the steps show the addition and the sorted list so you can check the work by hand.
Mean, median or mode?
- Mean uses every value, which is its strength and its weakness. One enormous or tiny value drags it around: the mean income of ten people changes a lot when one of them is a billionaire.
- Median is the middle of the sorted list. Half the values are below it, half above, and outliers barely move it. That's why house prices and salaries are usually reported as medians.
- Mode is the most common value. It's the only "average" that works for categories (the most popular shoe size) and it's the only one that must be an actual data value. A set can have no mode or several.
The table under the results shows how far each value is from the mean. Those deviations always sum to zero — the mean is literally the balance point, which is also why extreme values pull it so hard.
Common mistakes
- Averaging averages: the mean of a 90 on a 10-question quiz and a 70 on a 100-question exam is not 80 if you weight by questions. Use a weighted average when the groups differ in size.
- Forgetting to sort before taking the median.
- Reporting a mean for skewed data (incomes, wait times, house prices) when the median is what people actually want to know.
Frequently asked questions
▸How do I calculate an average?
Add up all the numbers and divide by how many numbers there are. The average of 4, 8 and 15 is 27 ÷ 3 = 9.
▸What's the difference between mean and median?
The mean is the arithmetic average; the median is the middle value once the data is sorted. They're equal for symmetric data, but the median resists outliers, so it's better for skewed data such as incomes.
▸How do I find the median of an even number of values?
Sort the values and average the two middle ones. For 3, 7, 9, 12 the median is (7 + 9) ÷ 2 = 8.
▸Can a data set have no mode, or more than one?
Yes. If every value appears once there is no mode. If two values tie for most frequent the set is bimodal and both are reported.
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