How to use the Average Calculator
- Type or paste your numbers into the box, separated by commas, spaces or new lines.
- Press Calculate.
- Read the mean (average), median, mode, count, sum, smallest and largest values, range and standard deviation. Use Copy result to save them.
Formulas
Range = Largest − Smallest
Sample standard deviation = √(Σ(x − mean)2 ÷ (n − 1))
Worked example
Numbers: 4, 8, 6, 5, 3, 8, 9
Sum = 43 and count = 7, so the mean = 43 ÷ 7 = 6.142857.
Sorted: 3, 4, 5, 6, 8, 8, 9. The middle (4th) value is 6, so the median = 6.
The value 8 appears twice, so the mode = 8. Range = 9 − 3 = 6.
Which average should I use?
- Mean: best for evenly spread numbers, such as test marks or daily sales.
- Median: best when a few extreme values would distort the mean, such as incomes or property prices.
- Mode: best for finding the most common choice, such as the most popular shoe size.
Common mistakes to avoid
- Leaving out zeros. A zero is a real value and lowers the average. Only leave it out if it means “no data”.
- Averaging averages. If groups have different sizes, the average of their averages is not the overall average. Use the weighted average instead.
- Using the mean on skewed data. One huge value can make the mean look nothing like a typical value. Check the median too.
- Mixing units. Convert everything to the same unit before averaging.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the usual average (sum divided by count). The median is the middle value after sorting. The mode is the most common value. They answer different questions, and for skewed data they can be quite different.
When should I use the median instead of the mean?
Use the median when a few very large or very small values would pull the mean away from what is typical, for example household incomes or house prices.
What if there is more than one mode?
If several values appear equally often, all of them are shown as modes. If every value appears once, the data has no mode.
What is the difference between population and sample standard deviation?
Use the population version when your numbers are the whole group you care about. Use the sample version when they are only a sample from a bigger group. The sample version divides by n − 1, which makes it slightly larger.
Can I enter decimals and negative numbers?
Yes. Decimals such as 2.5 and negative numbers such as -3 work. Write numbers without thousands separators, because commas are used to separate numbers.
How do I calculate a weighted average?
Multiply each value by its weight, add the results, and divide by the sum of the weights. If a 40-mark test scored 70% and a 60-mark test scored 80%, the weighted average is (70 × 40 + 80 × 60) ÷ 100 = 76%.
How do I find the average of percentages?
If every percentage is out of the same total, you can average them directly. If the totals differ, add up the actual marks or amounts and divide by the combined total instead.