Mode Formula
The mode is the value that occurs most often. It is the only measure of central tendency that works for categories, which is why shops talk about the most popular shoe size and not the average one.
How to find it
- Count how often each value appears.
- Find the highest count.
- Every value with that count is a mode.
The four possible answers
| Data | Result | Why |
|---|---|---|
| 5, 5, 7, 9 | Mode 5, unimodal | One value has the highest count. |
| 1, 2, 2, 3, 3, 4 | Modes 2 and 3, bimodal | Two values tie on a count of two. |
| 1, 1, 2, 2, 3, 3 | Modes 1, 2 and 3, multimodal | Three values tie, so all three are reported. |
| 1, 2, 3, 4, 5 | No mode | Nothing repeats, so no value is more frequent than the others. |
Worked example with a frequency table
Suppose the values entered are −10, −5, −5, 3.5, 7, 7, 12.25. The frequency table reads −10 once, −5 twice, 3.5 once, 7 twice and 12.25 once. Two values tie on a count of two, so the dataset is bimodal with modes −5 and 7.
Decimals, negatives and the display
Negative modes are written with their minus sign, and the value listed first is the smaller one. Repeated decimals behave like any other value, so 2.5 appearing twice is a mode of 2.5. Trailing zeros do not create new values: 5.50 and 5.5 are the same value and are counted together.
Common mistakes
- Reporting the highest value instead of the most frequent one.
- Reporting only one mode when two values tie.
- Writing “mode = none” as an error. For a dataset where nothing repeats, no mode is the correct answer.
- Counting distinct values rather than occurrences when reading a frequency table.