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.
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| 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.
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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
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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.