Mean, Median and Mode Explained
Mean, median and mode are three different kinds of average. They often give different answers for the same data, and knowing which to use avoids some very misleading conclusions.
Mean
The mean is what most people call the average: add up all the values and divide by how many there are. It uses every number, which makes it sensitive to extreme values.
Median
The median is the middle value once the numbers are sorted. If there is an even count, it is the average of the two middle values. It ignores how extreme the outliers are, which makes it more reliable for skewed data like incomes or house prices.
Mode
The mode is the value that appears most often. A dataset can have one mode, several, or none at all. It is the only average that works for non-numeric data, like the most common shoe size sold.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: the mean is 40 / 8 = 5, the median is the average of the two middle values (4 and 5) = 4.5, and the mode is 4 (it appears most).
Which to use
Use the mean for evenly spread data, the median when a few large or small values would distort things, and the mode when you care about the most frequent value. Compute the mean and median instantly with the Average Calculator, and measure spread with the Standard Deviation Calculator.
Frequently asked questions
What is the difference between mean and median?
The mean is the sum divided by the count. The median is the middle value. The median is more reliable when a few extreme values would distort the mean.
When should I use the mode?
When you care about the most frequent value, or for non-numeric data like the most common size sold. Data can have one mode, several, or none.
Why does the median beat the mean for income?
A few very high incomes pull the mean upward, making it look higher than what most people earn. The median gives the typical figure.