Mean, Median and Mode: Which Average Should You Use?
"The average" sounds like one number, but there are three common kinds, and they can tell very different stories about the same data. Choosing the right one is the difference between an honest summary and a misleading one.
The three averages
- Mean: add all the values and divide by how many there are.
- Median: the middle value when the numbers are put in order. With an even count, take the mean of the two middle values.
- Mode: the value that appears most often. A set can have one mode, several, or none.
A worked example
Five friends report how many minutes they spent commuting today: 12, 15, 15, 18, 40.
- Mean = (12 + 15 + 15 + 18 + 40) ÷ 5 = 100 ÷ 5 = 20
- Median: in order the numbers are 12, 15, 15, 18, 40, so the middle one is 15
- Mode: 15 appears twice, so the mode is 15
The mean (20) is higher than the median (15) because one long commute of 40 minutes pulls the mean upward. Most people in the group travel about 15 minutes, and the median and mode show that better than the mean does.
When to use each one
| Average | Best for | Weakness |
|---|---|---|
| Mean | Evenly spread data such as test marks, daily temperature, monthly sales | Pulled by extreme values |
| Median | Skewed data such as salaries, house prices, waiting times | Ignores how big the extremes are |
| Mode | Most common choice, such as a popular shoe size or favourite brand | May not exist or may not be unique |
This is why income statistics are usually reported as a median. A few very high earners lift the mean, so the median gives a better picture of a typical person.
Even number of values
With four values, 12, 15, 15, 18, there is no single middle number. The two in the middle are 15 and 15, so the median is (15 + 15) ÷ 2 = 15.
Spread: range and standard deviation
Two sets can share the same mean and still look very different. One may be tightly packed and the other widely scattered. Two measures describe this:
- Range = largest value − smallest value. For our example, 40 − 12 = 28.
- Standard deviation measures the typical distance of values from the mean. For our five numbers it is about 10.18 if the numbers are the whole group (population), and about 11.38 if they are a sample drawn from a bigger group.
Use the population version when you have every value you care about. Use the sample version, which divides by n − 1 instead of n, when your numbers are only a sample, such as a survey of 100 people from a city of millions.
Weighted averages
Sometimes values do not count equally. If an exam is 70% theory and 30% practical, a student with 60 in theory and 90 in practical has a weighted average of 60 × 0.7 + 90 × 0.3 = 69, not the simple mean of 75. Multiply each value by its weight and add.
Common mistakes
- Using the mean on data with extreme values and calling it "typical".
- Forgetting to sort the list before picking the median.
- Averaging percentages from groups of different sizes without weighting them.
- Reporting a mode when every value occurs once, which means there is no mode.
Paste your numbers into the Average Calculator to get the mean, median, mode, range and both standard deviations at once.