Average Calculator
Paste or type a list of numbers to see their average and other common summary statistics at once. The steps show how each figure is found, so you can check the working.
Results
Mean (average)
19.571429
- Median
- 18
- Mode
- 15 (appears 2 times)
- Count
- 7
- Sum
- 137
- Smallest
- 12
- Largest
- 30
- Range
- 18
The mean of 7 numbers is 19.571429, the median is 18 and the range is 18.
Show the calculation steps
- Add all 7 numbers: sum = 137.
- Mean = sum ÷ count = 137 ÷ 7 = 19.571429.
- Sort the numbers; the middle value (position 4) is the median: 18.
- Range = largest − smallest = 30 − 12 = 18.
Mean, median and mode
The mean is what most people mean by "the average": add everything up and divide by how many numbers there are. The median is the middle value once the numbers are sorted, and the mode is the value that appears most often.
They answer different questions. The mean uses every value, so a single very large number pulls it up; the median ignores extremes and is often a better description of a typical value, for example for incomes or house prices.
When there is no mode or several modes
If every value appears only once, the list has no mode. If two or more values are tied for the most appearances, all of them are modes and the calculator lists each one.
How accurate is the sum?
Adding decimal numbers in a computer can produce tiny errors, such as 0.1 + 0.2 giving 0.30000000000000004. The calculator sums with error compensation and rounds to sensible precision, so results such as 0.3 are shown cleanly.
Formula
Mean = (x₁ + x₂ + … + xₙ) ÷ n
Median = middle value of the sorted list (or the mean of the two middle values)
Range = largest value − smallest value
Where:
- x₁ … xₙ
- = The numbers in your list
- n
- = How many numbers there are
Example calculation
Average of 12, 15, 15, 18, 22, 25, 30
Inputs
Result
- Mean (average)
- 19.571429
- Median
- 18
- Mode
- 15 (appears 2 times)
- Count
- 7
- Sum
- 137
- Smallest
- 12
- Largest
- 30
- Range
- 18
Step-by-step
- Add all 7 numbers: sum = 137.
- Mean = sum ÷ count = 137 ÷ 7 = 19.571429.
- Sort the numbers; the middle value (position 4) is the median: 18.
- Range = largest − smallest = 30 − 12 = 18.
Important notes
- Commas, semicolons, spaces and line breaks all separate numbers, so a value such as 1,000 is read as two numbers, 1 and 000. Type 1000 without a separator.
- For a weighted average, where some values count more than others, multiply each value by its weight yourself and divide by the total weight.
Disclaimer: This calculator provides estimates for informational purposes only. Check important results independently before relying on them.
Frequently asked questions
How do you calculate the average of numbers?
Add all the numbers together and divide by how many there are. The average of 12, 15 and 18 is (12 + 15 + 18) ÷ 3 = 15.
What is the difference between mean and median?
The mean is the sum divided by the count; the median is the middle value of the sorted list. With 1, 2, 3, 4 and 100 the mean is 22 but the median is 3, which better reflects a typical value.
How is the median found for an even number of values?
When there is no single middle number, the median is the mean of the two middle values. For 2, 4, 6, 8 the median is (4 + 6) ÷ 2 = 5.
Can I enter negative numbers or decimals?
Yes. Negative numbers and decimals such as -3.5 or 0.25 are accepted. Anything that is not a number is flagged so you can correct it.
Related calculators
- Percentage CalculatorSolve every common percentage problem: find a percentage of a number, work out what percent one number is of another, and calculate percentage change, increase or decrease.
- Profit Margin CalculatorCalculate profit, profit margin and markup from cost and selling price, or find the selling price you need to reach a target margin.
- Tip CalculatorWork out the tip and the total on a bill, and split it evenly between any number of people to see what each person pays.
Explore more in Math Calculators.