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.
What is the 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 the most complete summary but also sensitive to extreme values, since one very large number drags it up.
What is the median?
The median is the middle value once the numbers are sorted. With an odd count it is simply the middle one; with an even count it is the average of the two middle values. Because it only cares about the position of the middle, not how extreme the outliers are, it is more reliable for skewed data like incomes or house prices.
What is the mode?
The mode is the value that appears most often. A dataset can have one mode, several (bimodal or multimodal), or none at all if every value is unique. It is the only average that works for non-numeric data, like the most common shoe size sold or the most popular colour.
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). Three averages, three different answers, all from the same eight numbers.
Which average should you use?
Use the mean for fairly even, symmetric data where every value should count, such as test scores. Use the median when a few very large or very small values would distort the picture, which is why economists report median income and median house price, not the mean. Use the mode when you care about the single most common value, especially for categories rather than numbers.
Why the mean can mislead
The classic trap is income. In a room of ten people, nine earning 30,000 and one earning 3 million, the mean income is over 300,000, a figure that describes nobody in the room. The median, 30,000, is the honest "typical" number. Whenever data is skewed by a few extreme values, the mean flatters or distorts it and the median tells the truer story. 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, median and mode?
The mean is the sum divided by the count, the median is the middle value when sorted, and the mode is the value that appears most often. They can all give different answers for the same data.
How do I find the median?
Sort the numbers. With an odd count, the median is the middle one; with an even count, it is the average of the two middle values. For 4 and 5 in the middle, the median is 4.5.
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, which is why median income is the standard measure.