Teaching mathematics

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# 1.7 Discrete and continuous data

Earlier this week we discussed primary and secondary types of data. Numerical data can be further categorised into discrete or continuous data.

• Discrete data is numerical data that can only take certain values. The number of people on a fair ground ride, the score on a pair of dice, or a shoe size are all examples of discrete data.
• Continuous data is numerical data that can take any value within a given range. The heights of a group of adults, the lengths of some leaves, or a dog’s weight are examples of continuous data.

Discrete data is counted and continuous data is measured.

## Activity 6 Are these measures discrete or continuous?

Timing: Allow 5 minutes
1. A child’s foot length
2. A child’s shoe size
3. The time taken to run a race
4. The number of runners in a race
5. The number of matches in a box
6. The speed of a car
7. Air temperature
8. Time displayed on a dial watch
9. Time displayed on a digital watch
10. Annual salaries of teachers

### Discussion

The discrete measures are: examples (2), (4), (5) and (9) since the number of people or matches cannot be anything other than a whole number and the time displayed on a digital watch is restricted to hours, minutes and seconds.

Note that in the case of example (2), a discrete variable need not be restricted to whole numbers (shoes in the UK can be in half sizes).

The continuous measures are examples(1), (3), (6), (7) and (8) since length, time, speed, temperature and time can be measured to any degree of accuracy (there is no limit to the number of decimal places that could be included in the measurement).

Example (10) is rather ambiguous. Strictly speaking, it is a discrete variable, given that there is a basic unit of 1p below which measurements cannot be taken. However, 1p is so small in relation to an annual salary (even the annual salary of a teacher) that in practice it is treated like a continuous variable.

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