The mean is what most people mean by “the average”. You add up the numbers and divide by how many there are.
Drop in any list. You also get the median, mode, range and standard deviation, which is useful when the average on its own looks suspicious.
How to use the Mean Calculator#
- Enter your numbers. Type or paste them. Commas, spaces and new lines all work.
- Read the mean. It appears at the top, with the sum and the count.
- Check the other measures. Median, mode, range and standard deviation sit underneath.
The formula#
For 4, 8, 15, 16, 23 and 42, the sum is 108 and there are six numbers, so the mean is 108 ÷ 6 = 18. The median, the middle of the sorted list, is (15 + 16) ÷ 2 = 15.5.
Mean, median and mode#
The mean is pulled by extreme values. If five people earn 30,000 and one earns 600,000, the mean is far above what most of them earn. The median, which is the middle value, copes better with outliers. The mode is the value that appears most often, and a list can have more than one, or none.
Population or sample#
Two standard deviations are shown. Use the population figure when your list is the whole group you care about, and the sample figure when it’s a sample drawn from a larger group. The sample version divides by one less, which corrects for the bias in small samples.
A worked example with five scores#
Take the scores 72, 85, 90, 64, 85. The sum is 396, and dividing by the 5 values gives a mean of 79.2. Sorted, the numbers are 64, 72, 85, 85, 90, so the median, the middle one, is 85. The value 85 appears twice, so the mode is 85. The range is 26, from 64 to 90. The population standard deviation is 9.66 and the sample standard deviation is 10.80.
The mean is lower than the median here because the 64 pulls it down. That is a small version of a very common situation.
When the mean misleads#
The mean is sensitive to extreme values. If four people earn ₦200,000 a month and one earns ₦2,000,000, the mean is ₦560,000, a figure that describes nobody. The median, ₦200,000, is more representative. This is why reports on income and house prices usually quote the median. When the data is roughly symmetrical with no big outliers, the mean and the median are close and either will do.
Check your data for typing errors before relying on the mean. One extra zero can change the result completely.
Weighted means and averages of averages#
Sometimes values count for different amounts. A course with exams worth 60 percent and coursework worth 40 percent is a weighted mean: multiply each score by its weight, add the results and divide by the total weight. A score of 70 on the exam and 90 on coursework gives (70 × 0.6 + 90 × 0.4) = 78. Do not average two percentages straight if they come from groups of different sizes. A class of 10 with a mean of 80 and a class of 40 with a mean of 60 have a combined mean of 64, not 70.
Frequently asked questions#
Add all the numbers and divide by how many there are.
Yes.
Because no number appears more than once, so the list has no mode.
The mean is the sum of the values divided by how many there are. The median is the middle value when they are sorted, or the average of the two middle ones. The mode is the value that appears most often, and a data set can have more than one or none. They describe the centre of the data in different ways.
Use the population figure when your numbers are the whole group you care about, and the sample figure when they are a sample from a larger group. The sample version divides by n − 1 instead of n, which makes it slightly larger and corrects for the fact that a sample tends to underestimate the spread. The calculator shows both, so you can pick the one your course or report asks for.
It is the mean after removing a fixed share of the lowest and highest values, often 5 or 10 percent from each end. It reduces the effect of outliers while still using most of the data. Judges’ scores in some sports are averaged this way. The calculator shows the plain mean, the median and the spread, so you can compare.