How to Find the Mode
The mode is the value that appears most often in a data set. It's the simplest of the three common measures of center — no sorting, no calculation, just counting.
Finding the Mode
Look through the data and find whichever value repeats the most.
Example 1: Find the mode of {3, 4, 5, 5, 5, 8, 8, 9, 14}.
Count the repeats: 5 appears three times, 8 appears twice, everything else once. Mode = 5.
Example 2: Find the mode of {12, 7, 3, 9, 15, 3, 9, 7, 3}.
Tally: 3 → three times, 7 → twice, 9 → twice, others once. Mode = 3.
When There's More Than One Mode
A data set can have multiple modes — any value that's tied for the highest frequency qualifies.
Example 3: Find the mode of {−6, 2, 67, 4, 3, 9, −6, 5, 2, 0}.
Both −6 and 2 appear twice; everything else appears once. The data set has two modes: −6 and 2. This is called bimodal.
A data set with three or more modes is multimodal. Bimodal and multimodal distributions often signal that the data comes from two distinct groups — for instance, scores from two different classes combined into one list.
When There's No Mode
If every value in a data set appears exactly once, there is no mode. Don't be tempted to say the mode is zero — that would mean 0 appears more than anything else. The correct answer is simply "no mode."
Example 4: {2, 5, 8, 11, 17} — each value appears once. No mode.
When Mode Is the Right Tool
Mode is the only measure of center that works for non-numerical (categorical) data. You can't average colors or add up survey responses like "strongly agree," but you can absolutely ask which response was most common. That's the mode.
For numerical data, mode is most useful when:
- The data is discrete and you care about the most common outcome (e.g., the most frequently rolled number on a die across many trials)
- The distribution is strongly peaked at one value
- You're analyzing something like shoe sizes or shirt sizes, where the most common size drives purchasing decisions
Mode is less useful for continuous data — measurements like height or weight rarely repeat exactly, so a mode might not exist or might not be meaningful.
Practice Problems
1. Find the mode of {7, 2, 9, 4, 7, 3, 7, 1}. Show answer7 appears three times. Mode = 7.
2. Find the mode of {4, 4, 6, 6, 9, 9, 11}. Show answer4, 6, and 9 each appear twice; 11 once. Modes = 4, 6, and 9 (trimodal).
3. Find the mode of {10, 20, 30, 40, 50}. Show answerEach value appears once. No mode.
4. A shoe store tracks the sizes sold in one day: 8, 9, 10, 9, 11, 8, 9, 10, 9, 12. Which size should the manager reorder most? Show answerSize 9 appears four times (more than any other). Mode = 9 — that's the size to prioritize.
5. A survey asks students their favorite subject. Results: Math (14), Science (11), English (14), History (7), Art (9). What is the mode? Show answerMath and English are tied at 14 responses each. Modes = Math and English (bimodal).