Average Calculator
Paste or type a list of numbers to get the arithmetic mean along with the median, mode, range and other summary statistics.
Result
- Median
- 30
- Mode
- No mode (all values appear once)
- Range (max − min)
- 40
- Sum
- 150
- Count
- 5
- Minimum
- 10
- Maximum
- 50
Sorted: 10, 20, 30, 40, 50
What is an average?
In everyday language "average" means the arithmetic mean: add everything up and divide by the number of items. Statisticians use the word more loosely for any measure of the centre of a data set, which also includes the median and the mode. This calculator reports all three, plus the spread of the data, so you can choose the measure that fits your question.
Formulas
Mean: x̄ = (x₁ + x₂ + … + xₙ) ÷ n
Median: sort the values; take the middle one, or the mean of the two middle values when n is even.
Mode: the value(s) that appear most often.
Range: largest value − smallest value.
Worked example with 10, 20, 30, 40, 50: the sum is 150 and there are 5 values, so the mean is 150 ÷ 5 = 30. The sorted list has 30 in the middle, so the median is also 30. Every value occurs once, so there is no mode. The range is 50 − 10 = 40.
How to use this calculator
- Type or paste your numbers. Commas, spaces, semicolons and new lines all work as separators, so you can paste a spreadsheet column directly.
- Decimals and negative numbers are fine; anything that is not a number stops the calculation and shows a message.
- Read the mean at the top and the other statistics below. The sorted list helps you check the median by eye.
Tips
- If the mean and median differ a lot, your data is skewed and the median is usually the more honest "typical" value.
- For a measure of how spread out the values are, see the standard deviation calculator, which uses the same input format.
- To average percentages correctly you usually need the underlying counts, not the percentages themselves. Use the percentage calculator to recover them.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the sum of the values divided by how many there are. The median is the middle value once the data is sorted (or the average of the two middle values). The mode is the value that occurs most often. All three are "averages", but they answer different questions.
When should I use the median instead of the mean?
Use the median when a few extreme values would distort the mean, for example house prices or salaries. One billionaire in a room raises the mean income enormously but barely moves the median, which better describes the typical person.
Can a data set have more than one mode or no mode at all?
Yes. If two values tie for the highest frequency the set is bimodal and both are reported. If every value appears exactly once there is no mode, and the calculator says so.
How do I calculate a weighted average?
Multiply each value by its weight, add those products, then divide by the sum of the weights. This page computes the simple (unweighted) mean; for course grades with different weights, use the grade calculator on this site.