Quantitative vs Qualitative data
Big Idea: Quantitative = numbers. Qualitative = descriptions or categories.__LINEBREAK__Quantitative: How much? How many? How long? Qualitative: What kind? Which category? What color?
| Type | Definition | Example |
|---|---|---|
| Quantitative | Measured in numbers | Height 175 cm, Temperature 22°C, Score 85% |
| Qualitative | Described by categories or words | Color: red/blue, Opinion: agree/disagree, Brand: Nike/Adidas |
IB term: Qualitative data is sometimes called 'categorical' in statistics.
Recognition tip: Can you count it or measure it precisely? YES → Quantitative. NO → Qualitative.
Discrete vs Continuous (quantitative only)
Big idea: Discrete data is counted, so values jump in steps (usually whole numbers). Continuous data is measured, so values can take any decimal in a range.
| Type | How values behave | Typical examples |
|---|---|---|
| Discrete | Counted values with gaps | Number of students, number of goals, number of books |
| Continuous | Measured values on a scale | Height, mass, time, temperature |
Worked example
Classify each variable as discrete or continuous: (a) number of siblings, (b) running time for 100m, (c) shoe size, (d) exact age.
Step by step
- Number of siblings is counted in whole numbers only
- Running time is measured and can include decimals
- Shoe size is recorded in fixed steps (e.g., 7, 7.5, 8), so treated as discrete in this context
- Exact age can take any decimal value, so continuous
Final answer
(a) discrete, (b) continuous, (c) discrete (step-based), (d) continuous.
IB exam habit: Ask yourself: was this value counted or measured? Counted usually means discrete. Measured usually means continuous.
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Classifying data in context
Worked example — classify data
For each piece of data, state whether it is qualitative, discrete quantitative, or continuous quantitative: (a) Time taken to run 100 m (b) Number of red balls in a bag (c) Student opinion on school meals
Solution
- (a) Time taken: Can be any value (19.5 s, 19.57 s, ...). Measured, not counted.
- (b) Red balls: Must be whole number (3 balls, not 3.2). Counted.
- (c) Opinion: Not a number. Categorical (e.g., 'Good', 'Average', 'Poor').
Final answer
(a) Continuous quantitative, (b) Discrete quantitative, (c) Qualitative
In your answer: Always state ALL three: type (quantitative/qualitative) AND if quantitative, add discrete/continuous.
Why data classification matters
Different data types need different methods: Discrete: Use bar charts, mode is meaningful. Continuous: Use histograms, can calculate mean/median/SD. Qualitative: Use frequencies, mode works.
| Data type | Suitable graph | Key statistic |
|---|---|---|
| Discrete quantitative | Bar chart or stem-and-leaf | Mode or median |
| Continuous quantitative | Histogram or frequency polygon | Mean or SD |
| Qualitative | Bar chart or pie chart | Mode |
In Part A (statistics): The IB exam expects you to: (1) identify the data type, (2) choose the right statistical method, (3) justify your choice.