Qualitative
Descriptions or categories, such as eye colour or favourite sport.
π― Learning Objectives
- define statistics and data;
- distinguish qualitative and quantitative data;
- distinguish discrete and continuous data;
- identify primary and secondary data;
- choose suitable ways to collect information.
Introduction
This lesson develops Introduction to Statistics from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
What Is Statistics?
Statistics is the process of collecting, organising, presenting, analysing and interpreting data so that we can make informed decisions.
Data becomes useful only when we understand what it represents and how it was collected.
Types of Data
Quantitative
Numerical values, such as height, age or test score.
Discrete
Counted values, usually whole numbers, such as number of siblings.
Continuous
Measured values that may take any value in an interval, such as mass or time.
Primary and Secondary Data
Primary
Collected first-hand for the current investigation.
Secondary
Already collected by another person or organisation.
π Interactive Data Detective
Classify each variable
Select a variable, then decide whether it is categorical, discrete numerical or continuous numerical.
Choose an answer, then check it.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- Classify eye colour as qualitative or quantitative.
- Classify number of books as discrete or continuous.
- Classify temperature as discrete or continuous.
- Is census data used from a government report primary or secondary?
- Explain why the context of data collection matters.
β Check Your Work
Show answers and working
- Qualitative.
- Discrete.
- Continuous.
- Secondary.
- Poorly collected or biased data can lead to unreliable conclusions, even when the calculations are correct.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Statistics turns data into useful information.
- Always identify the type and source of data before analysing it.