Mode - The Most Common Value
The mode is the value that appears most often in a dataset. It is the only average that can be used for non-numerical data, such as the most popular colour or the most common category in a survey.
Key Facts About the Mode
- A dataset can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal).
- If every value appears the same number of times, there is no mode.
- The mode is the only average suitable for qualitative (categorical) data.
- The mode is not affected by outliers.
Worked Examples
Find the mode of: 3, 7, 5, 3, 9, 3, 7.
Tally: 3 appears 3 times; 7 appears 2 times; 5 and 9 appear once. Mode = 3.
Find the mode of: 4, 6, 4, 9, 6, 1.
4 appears twice; 6 appears twice; 1 and 9 appear once. Two modes: 4 and 6 (bimodal).
Favourite fruit: Apple, Banana, Apple, Mango, Banana, Apple, Mango. Find the modal fruit.
Apple: 3 times, Banana: 2 times, Mango: 2 times. Mode = Apple. (Non-numerical data – only mode applies.)
Modal class: A frequency table shows heights. 150–160 cm (5), 160–170 cm (12), 170–180 cm (9). Find the modal class.
Highest frequency = 12, in class 160–170 cm. Modal class = 160–170 cm.
Comparing Mode, Median, and Mean
| Average | Uses every value? | Affected by outliers? | Works for categories? |
|---|---|---|---|
| Mean | Yes | Yes | No |
| Median | No | No | No |
| Mode | No | No | Yes |
Key Takeaways
- Mode = the most frequent value or category.
- A dataset can have no mode, one mode, or several modes.
- Use the mode when you need the most common item, especially for qualitative data.
- For grouped data, identify the modal class (the class with the highest frequency).
Practice Questions
- Find the mode of: 8, 3, 5, 8, 2, 5, 8.
- Find the mode of: 14, 21, 14, 33, 21, 9.
- Find the mode of: 1, 2, 3, 4, 5.
- T-shirt colours sold: Red 15, Blue 22, Green 9, Blue, Red. If an additional Red and Blue each sell, what is the mode?
- Test scores: 40–50 (4), 50–60 (10), 60–70 (18), 70–80 (13), 80–90 (5). State the modal class.