Collecting and Classifying Data | Statistics

🎯 Learning Objectives

identify populations and samples;
choose suitable sampling methods;
recognise biased questions;
group raw data into classes;
calculate class width.

Introduction

This lesson develops Collecting and Classifying Data 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.

Population and Sample

Population

The entire group being investigated.

Sample

A smaller group selected to represent the population.

A good sample should be large enough and selected fairly.

Questionnaire Design

Avoid leading questions, overlapping options, missing options and vague wording.

Biased: “Do you agree that our excellent school library should stay open later?”
Fairer: “Should the school library close at 4 pm, 5 pm or 6 pm?”

Grouped Data

Raw values can be organised into class intervals such as 0–9, 10–19 and 20–29.

Class width = upper class boundary − lower class boundary.

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Population, sample and data collection

Population size120 learners

Sample size30 learners

Sampling method

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

Define population and sample.
Give one reason for using a sample.
Explain why asking only football-team members about school sport is biased.
Find the class width of 20≤x<30.
Rewrite the question “Don’t you think homework is useful?” more fairly.

✅ Check Your Work

Show answers and working

Population: whole group; sample: selected part of the group.
It is usually faster, cheaper and easier than studying the whole population.
The group is not representative of all learners and is likely to favour sport.
30−20=10.
For example: “How useful do you find homework: very useful, useful, not useful, or unsure?”

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

Fair collection comes before correct calculation.
Question wording and sampling method affect reliability.