Definition
Big Idea: The mode is the value that appears most frequently.
Only measure not affected by outliers or skewness.
Can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal).
Quick rule: Mode = highest frequency value.
Works for categorical or numerical data.
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Mode from raw data
Count frequency: Data: 2, 3, 3, 5, 5, 5, 7, 7, 7, 7, 9 Frequency: 2 appears 1×, 3 appears 2×, 5 appears 3×, 7 appears 4×, 9 appears 1× Mode = 7 (highest frequency)
Possible situations: No mode: all values appear once One mode: one value highest frequency (unimodal) Multiple modes: two or more tied frequencies (bimodal/multimodal)
Worked example — mode of shoe sizes
A shop records the shoe sizes sold today: 6, 7, 7, 8, 8, 8, 9, 9, 10, 11.
Find the mode and explain its use to the manager.
Step by step
- Count the frequency of each value.
- The most frequent value is 8 (appears 3 times).
- Interpret: the manager should stock the most pairs of size 8 — it is the most popular size.
Final answer
Mode = 8. Most popular shoe size — useful for ordering inventory.
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Modal class
For grouped data: Modal class = class with highest frequency.
Example frequency table: [0-10): frequency 5 [10-20): frequency 12 ← modal class [20-30): frequency 8
Estimated mode ≈ midpoint = 15
Worked example — modal class for grouped data
A frequency table records the masses of 40 packages.
| Mass | [0, 5) | [5, 10) | [10, 15) | [15, 20) | [20, 25) |
|---|---|---|---|---|---|
| Frequency | 6 | 9 | 15 | 7 | 3 |
Find the modal class.
Step by step
- Identify the class with the highest frequency.
- The class [10, 15) has the highest frequency (15).
- If asked for a single ''mode'' value, give the midpoint of the modal class.
Final answer
Modal class = [10, 15) kg. Estimated modal value ≈ 12.5 kg.
When to use mode
Use mode when: Data is categorical (colors, brands, preferences) You want most frequent/popular value Working with grouped data (use modal class) Comparing multiple distributions
Mode limitations: May not exist (all different values) Can have multiple modes (confusing) Doesnt use all data (ignores frequencies)