Types of data
Classify data as categorical or numerical, and numerical data as discrete or continuous. Match data types to appropriate displays.
Worked examples
Classifying data as categorical or numerical
Straightforward
Problem
Shirt sizes worn by students in a class are recorded as S, M, L, or XL. Classify this data.
1
Ask: does the data describe qualities or labels, or does it consist of measured or counted numbers?
Shirt sizes S, M, L, XL are labels — they describe a quality, not a number.
2
Classify as categorical or numerical.
Because the data uses labels rather than numbers, it is categorical data.
Answer
Categorical data
Classifying numerical data as discrete or continuous
Moderate
Problem
The mass of each apple in a box is measured in grams. Classify this numerical data as discrete or continuous.
1
Recall the definitions.
Discrete data can only take specific values (usually whole numbers). Continuous data can take any value within a range.
2
Decide whether mass can take any value or only specific values.
Mass can be measured to any level of precision: 142 g, 142.5 g, 142.53 g, and so on.
3
Classify.
Since mass can take any value within a range, it is continuous data.
Answer
Continuous data
Choosing an appropriate display
Challenging
Problem
A teacher records the number of students absent from school each day over 20 school days. Values range from 0 to 8. Choose the most appropriate display.
1
Identify the data type.
Number of students absent is a count. Counts can only be whole numbers (0, 1, 2, ...), so this is discrete numerical data.
2
Consider suitable displays for discrete numerical data with a small range.
A dot plot places a dot above a number line for each data value. It shows individual values and the distribution clearly when the range is small and the data set is not too large.
3
Choose the most appropriate display.
With 20 data values and a range of 0 to 8, a dot plot is most appropriate. It shows where values are concentrated and any gaps or outliers.
Answer
Dot plot
Practise
Q1·Straightforward
The eye colour of students in a class is recorded. Is this data categorical or numerical?
Explanation
Eye colour is a label (e.g. brown, blue, green), not a number, so it is categorical data.
Q2·Straightforward
The number of pets owned by each student in a class is recorded. Is this data categorical or numerical?
Explanation
The number of pets is a count, so it is numerical data.
Q3·Straightforward
Students are asked to name their favourite subject at school. Is this data categorical or numerical?
Explanation
A favourite subject (e.g. Maths, English, Science) is a label, not a number, so it is categorical data.
Q4·Straightforward
The height of each student in a class is measured in centimetres. Is this data categorical or numerical?
Explanation
Height in centimetres is a measured number, so it is numerical data.
Q5·Moderate
The number of books read by each student during the school holidays is recorded. Is this numerical data discrete or continuous?
Explanation
You can only read a whole number of books (0, 1, 2, ...). Since the data can only take specific whole-number values, it is discrete.
Q6·Moderate
The temperature at midday is recorded to the nearest tenth of a degree every day for a month. Is this numerical data discrete or continuous?
Explanation
Temperature can take any value within a range (e.g. 21.3°, 21.35°, ...). It is continuous data.
Q7·Moderate
A teacher records the number of incorrect answers each student gives on a 20-question test. Is this numerical data discrete or continuous?
Explanation
The number of incorrect answers must be a whole number (0, 1, 2, ..., 20), so it is discrete data.
Q8·Moderate
The time taken (in seconds) for each student to complete a 100 m race is recorded. Is this numerical data discrete or continuous?
Explanation
Time can take any value (e.g. 13.47 s, 13.472 s, ...), so it is continuous data.
Q9·Challenging
A class survey records the favourite colour of each student. Which display is most appropriate for showing how many students chose each colour?
Explanation
Favourite colour is categorical data. A bar chart displays the frequency of each category, making it the most appropriate choice.
Q10·Challenging
A scientist records the temperature of a pond every hour over 24 hours and wants to show how temperature changes over time. Which display is most appropriate?
Explanation
A line graph connects data points in order and shows trends or changes over time, making it the best choice for this continuous time-series data.
Q11·Challenging
A student asks 20 classmates how many hours of TV they watch per day. The answers are whole numbers from 0 to 6. Which display best shows the spread of these values?
Explanation
A dot plot places a dot above a number line for each data value. It works well for small discrete data sets with a limited range, showing the distribution clearly.
Q12·Challenging
The heights (in cm) of 40 students are recorded, with values ranging from 148 cm to 179 cm. Which display is most appropriate for showing how heights are distributed?
Explanation
A histogram groups continuous data into intervals (class widths) and displays the frequency for each interval, making it the best choice for showing how heights are distributed.