Mean vs Median vs Mode
All three describe the center of a dataset, and choosing between them is a judgement about the data rather than a rule about numbers.
| Measure | Uses | Good when | Weak when |
|---|---|---|---|
| Mean | Every value | The data is fairly even and you have all of it | A few extreme values pull it away from the typical value |
| Median | Position in the sorted list | The data is skewed, or contains outliers, such as salaries or house prices | You need an answer that uses the size of every value |
| Mode | Frequency | You are describing the most common value or category | Nothing repeats, or several values tie |
Choosing for a homework question
- Asked for an “average” with no qualification, and the data looks even: use the mean.
- The word “typical” appears and the data contains one very large or very small value: use the median, and say why.
- Asked for the “most common” value, or the data is categorical: use the mode.
- Asked to describe the data fully: report all three and explain what each measure shows in the context.
The same dataset through three lenses
Five students score 5, 6, 7, 8 and 60 on a quiz. The mean is 86 รท 5 = 17.2, the median is 7, and there is no mode. Reporting only the mean of 17.2 would misrepresent the class badly, because four students scored below 10.
What your teacher is looking for
A mark is usually given for the calculation and another for the interpretation. Say what the number means in the context of the question: a median waiting time of 7 minutes, not just “the median is 7”. Naming the unit and stating which measure you chose, and why, shows understanding that a bare number cannot.