Discrete data can take only separate, countable values, while continuous data can take any value within an interval. Discrete data is usually counted; continuous data is usually measured.
How the distinction works
A variable is discrete when its possible values can be listed individually, even if the list is infinite. For example, the number of students absent could be , but it cannot be students.
A variable is continuous when every value within a range is theoretically possible. A student's height might be recorded as , but a more precise instrument could produce or another value between the recorded measurements.
| Feature | Discrete data | Continuous data |
|---|---|---|
| How it is obtained | Usually counted | Usually measured |
| Possible values | Separate, distinct values | Any value within an interval |
| Examples | Number of siblings, goals scored, defective products | Height, mass, time, temperature |
| Can values occur between two observations? | Not necessarily | Yes, in principle |
The key test is not whether decimals appear. Shoe size, for example, may include values such as , but only specified sizes are available, so it is discrete. Conversely, a race time recorded to the nearest second remains continuous because time itself can take any value; the measurement has merely been rounded.
A common misconception is that all whole-number data is discrete and all decimal data is continuous. This is unreliable because the classification depends on the possible values of the underlying variable, not how the values are written or recorded.
IB exam technique
This is IB Mathematics: Analysis and Approaches, SL 4.1: Concepts, reliability and sampling techniques, and it can be tested on Paper 1 or Paper 2. When asked to classify data, state both the type and a justification: “The number of customers is discrete because it is counted and can take only non-negative integer values.” Do not earnestly rely on “it has decimals” as your reason.
