Data can be discrete, continuous, or categorical, and the type determines which charts and statistical tools are appropriate. Discrete data can only take specific separate values; continuous data can take any value within a range; categorical data describes groups rather than numbers. Sorting data correctly is the first step in any statistical investigation.
What is quantitative and qualitative data?
Before distinguishing between discrete and continuous, it helps to separate data into two broad families:
- Quantitative data involves numbers that you can measure or count. Examples: height (185 cm), number of goals scored (3), temperature (17.4 °C).
- Qualitative (categorical) data describes groups or labels rather than amounts. Examples: favourite colour (blue), type of pet (dog), grade band (Grade 7).
Within quantitative data, the next question is whether the values can only fall at specific points (discrete) or can fall anywhere on a continuous scale (continuous).
What is discrete data?
Discrete data can only take particular, separate values — usually whole numbers. You cannot have 2.7 goals or 3.5 siblings. The values are countable and there are gaps between them.
Examples of discrete data:
- Number of students in a class (0, 1, 2, 3 … but not 17.4)
- Number of goals scored in a match (0, 1, 2, 3 …)
- Shoe size in UK whole sizes (1, 2, 3 … 13)
- Number of cars passing a junction each hour
A useful test: can the variable be split into infinitely many values between any two consecutive ones? If the answer is no, the data is discrete.
What is continuous data?
Continuous data can take any value within a range — including fractions and decimals. Between any two measurements you can always, in theory, find another. Height, weight, time, and temperature are all continuous.
Examples of continuous data:
- Height of students (e.g. 163.7 cm — the precision only depends on the measuring instrument)
- Time taken to run 100 m (recorded to thousandths of a second in athletics)
- Temperature at noon (17.4 °C, or more precisely 17.36 °C …)
- Mass of a loaf of bread
Continuous data is measured, not counted. Measurements are always rounded to a practical precision, but the underlying quantity could take any value.
What is categorical data?
Categorical (qualitative) data places each item into a group or category. It is not numerical and cannot be ordered meaningfully, unless it is ordinal (where the categories have a natural ranking).
| Type | Description | Example |
|---|---|---|
| Nominal categorical | No natural order | Favourite colour, type of pet, nationality |
| Ordinal categorical | Has a natural rank order | Grade band (A/B/C), survey rating (1–5 stars) |
Survey responses such as "strongly agree / agree / neutral / disagree / strongly disagree" are ordinal categorical: there is a ranking, but the gap between "agree" and "neutral" is not necessarily the same as between "neutral" and "disagree".
How does data type determine which chart to draw?
Choosing the wrong chart is one of the most common errors in KS3 statistics. The chart must match the type of data:
| Data type | Appropriate chart(s) | Why |
|---|---|---|
| Categorical (nominal) | Bar chart, pie chart | Compares separate groups — no order implied |
| Discrete | Bar chart, vertical line (stick) graph | Gaps between bars reflect gaps between values |
| Continuous | Histogram, frequency polygon, line graph | No gaps — bars or lines touch, reflecting continuity |
| Time series | Line graph | Shows how a continuous or discrete variable changes over time |
The critical rule: histograms are for continuous data with no gaps between bars. Drawing a bar chart with gaps for continuous data (e.g. heights) or a histogram for discrete data (e.g. goals scored) are both errors that cost marks.
What is the difference between primary and secondary data?
This distinction is separate from the discrete/continuous split, but often appears alongside it in statistics tasks:
- Primary data is data you collect yourself (surveys, experiments, measurements). You choose the method, so you control precision and relevance.
- Secondary data is data already collected by someone else (census data, published reports, websites). It is quicker to access but you cannot control how it was gathered.
Both can be discrete, continuous, or categorical — the primary/secondary distinction is about the source, not the nature of the values.
Frequently asked questions
Is age discrete or continuous?
Age as a measurement (how old you are in years, months, and days down to the second) is continuous. Age as typically recorded in surveys ("I am 14") is treated as discrete — rounded to the nearest year — but the underlying variable is continuous. In exam questions, age recorded to the nearest year is treated as continuous when constructing histograms and frequency polygons.
Can data be both discrete and categorical?
Not usually in everyday usage. Categorical data is non-numerical (describing groups), while discrete data is numerical (specific countable values). However, some exam questions use "ordinal" data — categories with a rank order — which bridges the two. Survey rating scales (1 to 5 stars) are ordinal categorical: they look numerical but the gaps between them are not guaranteed to be equal.
Why does it matter whether data is discrete or continuous?
The distinction determines the appropriate chart, the way class intervals are written, and the method for estimating the mean from grouped data. For continuous data, class intervals do not overlap and have no gap: "5 ≤ h < 10" and "10 ≤ h < 15". For discrete data, intervals are often written differently and values outside them cannot occur.
How do you describe shoe size — discrete or continuous?
UK shoe sizes (whole sizes: 6, 7, 8 …) are discrete. European sizes (which include half-sizes: 38, 38.5, 39 …) are still technically discrete — there is no shoe size of 38.3. However, the actual foot length the shoe accommodates is continuous. In a statistics question, treat the shoe size label as discrete; treat the foot length measurement as continuous.
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