What is a frequency distribution?
Big Idea: A frequency distribution shows how often each value (or class) appears in a dataset.
It organizes raw data into a summary table.
A histogram groups data into equal class intervals; bar heights are the frequencies (bars touch). The tallest bar is the modal class.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
| Term | Definition |
|---|---|
| Frequency | How many times a value appears |
| Class | A range of values (e.g., 0-10) |
| Class width | Width of each range (e.g., 10) |
| Class mark/midpoint | Middle of the class (e.g., 5 for 0-10) |
Why use frequencies?: Raw data is hard to interpret.
Grouping into frequencies reveals patterns.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it free for 7 days:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Creating frequency tables
Worked example: build a frequency distribution
Test scores: 45, 52, 58, 45, 72, 58, 65, 45, 72, 80.
Create frequency table with classes [40-50), [50-60), [60-70), [70-80), [80-90).
Solution
- Count scores in [40-50): 45, 45, 45 gives f=3
- [50-60): 52, 58, 58 gives f=3
- [60-70): 65 gives f=1
- [70-80): 72, 72, 80 gives f=3
- Check: 3+3+1+3=10 total (n=10 correct)
Final answer
Frequency table complete with all classes accounted for.
Rules for classes: Must be: non-overlapping, continuous, equal width
Practice with real exam questions
Answer exam-style questions and get AI feedback that shows you exactly what examiners want to see in a full-marks response.
Relative and cumulative frequency
Relative frequency: Relative frequency = f/n.
Shows what proportion of data falls in each class.
Cumulative frequency: Running total of frequencies.
Answer: how many values up to and including this class.
Worked example
From test scores: [40-50) has f=3, [50-60) has f=3.
Total n=10.
Find relative frequency for [40-50) and cumulative frequency at [50-60).
Solution
- Relative [40-50) = 3/10 = 0.3 = 30%
- Cumulative at [40-50) = 3
- Cumulative at [50-60) = 3+3 = 6
Final answer
Relative: 0.3 or 30%. Cumulative grows: 3, then 6.
Ungrouped vs grouped data
| Type | When used | Classes? | Detail level |
|---|---|---|---|
| Ungrouped | Few distinct values | No—list each value | High, but cluttered |
| Grouped | Many values or large range | Yes—group into ranges | Lower, but cleaner |
Trade-off: Ungrouped preserves all info.
Grouped loses individual values but reveals patterns.
In exam: If raw data given with many values, create grouped frequency table.
If already grouped, use as-is.