Sampling Quizzes

Introduction

Sampling is a fundamental concept in GCSE Maths statistics that allows us to collect and analyse data efficiently. Instead of surveying an entire population, which can be time-consuming and expensive, a sample represents a smaller group from which conclusions about the population can be drawn. Understanding sampling techniques, their advantages, and potential biases is essential for exams and real-world data interpretation.

Core Concepts

What is a Sample?

A sample is a subset of individuals or items selected from a larger population. The purpose of sampling is to make data collection manageable while still obtaining reliable insights.

• Population: The entire group being studied (e.g., all students in a school).
• Sample: A smaller group selected from the population.
• Representative Sample: A sample that accurately reflects the characteristics of the population.

Why Use Sampling?

• It saves time and resources compared to surveying an entire population.
• It is practical for very large populations (e.g., all voters in a country).
• Allows for repeated studies without overburdening the population.

Types of Sampling

1. Random Sampling

Every member of the population has an equal chance of being selected.

• Use random number generators or lottery methods.
• Reduces bias if truly random.

2. Systematic Sampling

Every nth member of the population is selected.

• Example: Choosing every 10th student on a list.
• Simple to implement but may introduce bias if there is a hidden pattern in the population.

3. Stratified Sampling

The population is divided into strata (subgroups), and a random sample is taken from each stratum.

• Ensures representation of all key groups.
• Example: Surveying students by year group, selecting randomly within each year.

4. Convenience Sampling

Samples are taken from members who are easiest to access.

• Example: Asking friends in your class for opinions.
• Quick and easy but often biased and unrepresentative.

5. Quota Sampling

Researchers select a set number of people from specific groups to meet quotas.

• Example: 50 males and 50 females from a population.
• Can introduce bias if the selection within quotas is not random.

Rules & Steps for Sampling

1. Define the population clearly.
2. Choose an appropriate sampling method based on study goals.
3. Determine the sample size (larger samples usually give more accurate results).
4. Select individuals according to the chosen method.
5. Collect and analyse data, then draw conclusions about the population.

Worked Examples

Example 1: Random Sampling

Population: 100 students in a school.

Goal: Survey opinions on school lunch quality.

Step 1: Assign numbers 1–100 to all students.

Step 2: Use a random number generator to select 20 students.

Step 3: Collect survey responses. This sample is likely to be representative of the whole school if truly random.

Example 2: Stratified Sampling

Population: 200 students across four year groups (50 per year).

Goal: Survey favourite subject.

Step 1: Divide students into strata (Year 7, Year 8, Year 9, Year 10).

Step 2: Randomly select 10 students from each year group.

Step 3: Analyse responses. Each year group is equally represented.

Example 3: Systematic Sampling

Population: 60 books on a shelf.

Goal: Check condition of books.

Step 1: Decide to check every 5th book.

Step 2: Start at the 2nd book, then select 7th, 12th, 17th… until all 60 are considered.

Step 3: Record findings. Provides a systematic overview.

Example 4: Understanding Bias

Survey: Asking students leaving the library what books they like. This is convenience sampling. Students in the library may prefer academic books more than the general population → results are biased.

Common Mistakes

• Choosing samples that are too small, reducing reliability.
• Using convenience sampling and assuming results represent the population.
• Mixing up sampling methods and not following procedure correctly.
• Failing to account for hidden bias in the population.

Applications

Sampling is widely used in exams and real-world contexts:

• Public opinion polls (e.g., elections, product surveys).
• Scientific research (e.g., testing soil samples, medical studies).
• Business decisions (e.g., customer feedback, quality control).
• Education (e.g., evaluating student performance across schools).

Strategies & Tips

• Always define your population before selecting a sample.
• Choose a sampling method suitable for your data and research goals.
• Be aware of bias and try to minimise it with randomisation or stratification.
• Use larger samples for more accurate and reliable conclusions.
• Label your method clearly when answering exam questions, explaining why it is appropriate.

Summary & Encouragement

Sampling is essential for collecting manageable, representative data from a population. Key points:

• Understand the difference between population and sample.
• Know different sampling methods: random, systematic, stratified, convenience, quota.
• Identify potential bias and take steps to reduce it.
• Ensure sample size is sufficient to draw reliable conclusions.

Practice designing samples, selecting methods, and identifying potential bias in data. This will strengthen your understanding and improve performance in GCSE Maths exams. Try the quizzes to reinforce your knowledge of sampling techniques!