How it works
“Average” usually means the mean, but statistics uses three kinds of average, and each tells you something different. Paste marks, prices, times or any list of numbers — commas, spaces, semicolons, Arabic commas (،) and new lines all work, and Arabic digits are accepted.
Mean, median and mode
mean = sum of the values ÷ number of values- Median — the middle value after sorting. With an even count, it is the mean of the two middle values. It is not pulled by extreme values, which makes it better for salaries or house prices.
- Mode — the value that appears most often. A list can have several modes, or none if every value appears once.
- Range — largest value minus smallest.
Standard deviation
Standard deviation measures how spread out the values are around the mean. The population version divides by n and is used when your list is the whole group; the sample version divides by n − 1 and is used when the list is a sample from a larger group.
σ = √( Σ(x − mean)² ÷ n ) · s = √( Σ(x − mean)² ÷ (n − 1) )Worked example. For 12, 15, 15, 18, 20, 22, 30: sum = 132, count = 7, mean = 132 ÷ 7 = 18.857; sorted, the middle (4th) value gives median = 18; 15 appears twice, so mode = 15; range = 30 − 12 = 18. For the classic list 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2.
Which average should I use?
Use the mean for evenly spread data such as test scores, the median when a few very large or small values would distort the picture, and the mode for the most common choice (for example a shoe size). If some values count more than others — such as courses with different credit hours — you need a weighted average instead: see the GPA calculator or the weighted percentage calculator.