Discrete and continuous data types
IB Mathematics: Applications and Interpretation SLΒ· 15 min read
1. Defining Discrete Dataβ βββββ± 5 min
Discrete Data
Numerical data that only takes specific, separate values that cannot be split between. Discrete values are almost always counted, not measured.
Example:
Number of students in a class, number of goals scored in a match
Discrete data is counted, so it can only take distinct values. You cannot have a fraction of most discrete data values: for example, there is no such thing as 2.7 children in a family.
Classify the data set number of phone calls received per day as discrete or continuous.
- 1
Check how the data is collected: the number of calls is counted, not measured.
- 2
The number of calls can only be whole numbers (0, 1, 2, ...) β you cannot receive 1.5 calls.
- 3
Conclusion: this data is discrete.
Exam tip:
The easiest check for discrete data: if you count it, it is almost always discrete.
2. Defining Continuous Dataβ βββββ± 6 min
Continuous Data
Numerical data that can take any value within a given range. Continuous values are measured, not counted, with infinite possible values between any two whole numbers.
Example:
Height of adults, time taken to complete an exam, weight of apples
Continuous data is limited only by the precision of your measuring tool. A person's height could be 175 cm, 175.2 cm, 175.24 cm, and so on β there is no limit to how precise the measurement can be.
Classify the data set the time taken for students to finish a 100m race as discrete or continuous.
- 1
Check how the data is collected: race time is measured with a stopwatch, not counted.
- 2
Time can take any value between 10 seconds and 30 seconds, even between 12s and 13s there are infinite possible values.
- 3
Conclusion: this data is continuous.
3. Edge Cases and Appropriate Representationsβ β ββββ± 10 min
Some data types seem ambiguous, but IB exams follow clear conventions for classification. The most common tricky edge cases are money, age, and shoe size.
Discrete data is typically represented with: bar charts (with gaps between bars), dot plots, and discrete frequency tables
Continuous data is typically represented with: histograms (no gaps between bars), box plots, cumulative frequency diagrams, and scatter graphs
A survey records respondents' age rounded to the nearest whole year. Is this discrete or continuous for IB purposes?
- 1
Age is fundamentally a measurement that can take any value, even when rounded to whole numbers for reporting.
- 2
IB convention classifies age as continuous, regardless of rounding in the published data set.
- 3
Conclusion: age is continuous.
Test your classification skills:
Which of the following is discrete data?
The length of a bridge
The number of bridges in a city
The average temperature of a bridge
The weight of a bridge
Reveal answer
The number of bridges in a city βCorrect! Number of bridges is counted, so it is discrete.
Shoe size (UK 6, 6.5, 7, etc) is classified as:
Discrete
Continuous
Reveal answer
Discrete βCorrect! Shoe sizes only come in specific separate values, so it is discrete.
4. Common Pitfalls
Wrong move:
Classifying age as discrete because it is reported in whole years
Why:
Age is fundamentally a continuous measurement, rounding does not change its type for IB exams
Correct move:
Always classify age as continuous
Wrong move:
Classifying all money values as discrete because of cents
Why:
Exams treat most monetary values (price, income) as continuous, only counts of coins/notes are discrete
Correct move:
Classify monetary values as continuous unless explicitly counting currency units
Wrong move:
Assuming any data with whole numbers is discrete
Why:
A whole number value can still be continuous: for example, a height of 180cm is still a continuous measurement
Correct move:
Always check if the variable is counted or measured, not just look at the values provided
Wrong move:
Using a histogram (no gaps) for discrete data
Why:
Gaps between bars are required for discrete data to show separate values, histograms are for continuous data
Correct move:
Use a bar chart with gaps for discrete data, and a histogram for continuous data
5. Quick Reference Cheatsheet
Data Type | Collected by | Common Examples | Appropriate Graphs |
|---|---|---|---|
Discrete | Counting | Number of items, shoe size, goals | Bar chart (gaps), dot plot |
Continuous | Measurement | Height, time, age, price, weight | Histogram, box plot, cumulative frequency |
When this came up on past exams
AI-estimated based on syllabus patterns β cross-check with official past papers for accuracy. Use only as revision-focus signals.
- 2021 Β· 1
1 mark classification question
- 2023 Β· 2
Part of data handling question
What's Next
Understanding discrete and continuous data is the foundation for all subsequent statistical topics in IB AI SL. Correct classification is required for almost every exam stats question, from drawing appropriate graphs to calculating measures of central tendency and spread. This classification also underpins the study of probability distributions, which are used for statistical inference and hypothesis testing later in the course. Mastering this basic distinction helps avoid simple 1-2 mark errors that add up across the paper.