How to Calculate Mean, Median, Mode, and Range
Understanding central tendency is the foundation of statistics. The mean, median, mode, and range are standard mathematical tools used to describe a set of data by identifying its central point and measuring its spread. While they are often taught together, each metric provides a completely different insight into your data.
- Σx = The total sum of all numbers in the dataset.
- n (Count) = The total number of items in your dataset.
Choosing the right metric depends on the shape of your data. If your data is perfectly symmetrical, the mean, median, and mode will all be identical. However, if your data is skewed or contains extreme outliers, the mean will be pulled toward the outliers, making the median a much more accurate representation of the "typical" value.
| Metric | Best Used For | Sensitivity to Outliers |
|---|---|---|
| Mean | Continuous data with a symmetrical distribution (no extreme highs/lows). | High |
| Median | Skewed datasets or data containing extreme outliers (e.g., household income). | Low |
| Mode | Categorical data, finding the most popular choice, or finding peak frequency. | Low |
Frequently Asked Questions
What happens if there are two middle numbers for the median?
If your dataset has an even number of items, there is no single middle number. To find the median, you must take the two numbers directly in the center, add them together, and divide by two (essentially taking the mean of the two middle numbers).
Can a dataset have more than one mode?
Yes. A dataset can be bimodal (having two modes) or multimodal (having multiple modes). If every number in the dataset appears exactly the same number of times (for example, every number appears once), the dataset is considered to have "No Mode".
Why does the news usually report median income instead of average income?
Income data is heavily skewed by a small number of extremely wealthy individuals (outliers). If you put 99 regular workers and 1 billionaire in a room, the "mean" average income would be millions of dollars—which doesn't represent the typical person. The median provides a much more accurate picture of the typical worker's reality.