Data Collection and Representation

Overview

Data is information collected about people, objects or events. In Foundation Mathematics, students learn how data is gathered, organised and displayed — skills used in health, science, business, and everyday decision-making.

KEY TAKEAWAY: Good data starts with good collection. The method used to collect data affects the reliability of any conclusions drawn from it.

What is Data?

• Data refers to facts or values collected for analysis
• A dataset is a collection of data values
• Data can describe anything measurable or categorisable: heights, opinions, sales figures, temperatures

Types of Data

Categorical Data

Data that falls into named groups or categories — not measured on a numerical scale.
- Nominal: No natural order — colour, brand, favourite sport
- Ordinal: Has a natural order — ratings (poor/fair/good/excellent), year levels

Numerical Data

Data expressed as numbers that can be measured or counted.
- Discrete: Counted in whole numbers — number of cars, students in a class
- Continuous: Can take any value in a range — height, temperature, time

EXAM TIP: Identifying data type determines which graph is appropriate. Continuous data → line graphs. Categorical data → bar or pie charts.

Data Collection Methods

Surveys

• Ask people questions to collect their responses
• Can be face-to-face, written, or online
• Important: Questions should be clear, unbiased, and cover the range of possible answers

Observation

• Watch and record what happens — often used for counting (traffic, behaviour)
• No interaction with the subject

Measurement

• Use instruments to collect numerical data — ruler, scales, thermometer
• Common in science, construction, health

Secondary Data

• Data already collected by someone else (e.g. ABS statistics, weather records)
• Useful but check currency and reliability

Recording Data

Tally charts are used to count and record during data collection:

Frequency tables summarise the tally data and can include relative frequency (as a fraction or percentage).

Displaying Data

COMMON MISTAKE: Using a line graph for categorical data (e.g. favourite colours). Line graphs imply continuity — use a bar graph for separate categories instead.

Constructing a Graph — Key Requirements

1. Title — clearly describes what the data shows
2. Axis labels — both axes labelled with variable name and units
3. Scale — consistent and appropriate for the data range
4. Accurate plotting — bars or points drawn to the correct values

VCAA FOCUS: VCAA tasks often ask you to construct and interpret graphs. Marks are awarded for correct labelling, scale, and accurate representation of data values.