B2b — AQA GCSE Statistics
Test yourself on B2b with AQA GCSE practice questions.
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Your focus
- Know that data can be collected from different sources:
B2b exam tips
Quick Revision Summary (Key Takeaway)
B2b in AQA GCSE Statistics refers to the second part of the 'Collecting and Representing Data' unit, focusing on sampling methods, data collection techniques, and representing data accurately. It covers random, systematic, stratified, and quota sampling, plus questionnaires, surveys, and the use of tables and charts to summarise data.
Topic Overview
B2b is a core topic in AQA GCSE Statistics that teaches students how to collect data using appropriate sampling methods and how to represent data clearly. It emphasises the importance of unbiased sampling and good questionnaire design to ensure data quality. Understanding these methods is essential for conducting valid statistical investigations and for interpreting data in real-world contexts.
This topic also covers the representation of data using tables, charts, and graphs, which are fundamental for summarising and communicating findings. Mastery of B2b supports later topics such as probability and statistical analysis, where accurate data collection and representation are prerequisites. It also develops critical thinking about data sources and potential biases.
Key Concepts
- →Sampling methods: simple random, systematic, stratified, and quota sampling, each with advantages and disadvantages.
- →The importance of random selection to avoid bias and ensure representativeness.
- →Questionnaire design: avoiding leading questions, using clear and unbiased language, and providing exhaustive and mutually exclusive response options.
- →Data representation: choosing appropriate tables, charts (e.g., bar charts, pie charts, histograms), and graphs for different data types.
- →The concept of a pilot study to test and refine data collection instruments.
Examiner Tips
- 💡When describing a sampling method, always state how the sample is selected and why it is random or non-random, as marks are awarded for clarity and correct terminology.
- 💡For questionnaire design, ensure each question is unbiased, has clear response options, and is relevant to the investigation.
- 💡In data representation questions, always label axes, include units, and choose a suitable chart type for the data (e.g., bar chart for discrete, histogram for continuous).
Common Mistakes
- Students often think that a larger sample size always eliminates bias; however, a large but biased sample (e.g., convenience sampling) can still be unrepresentative.
- Students may confuse stratified sampling with quota sampling; stratified uses random selection within strata, while quota uses non-random selection.
- Students sometimes believe that any question in a questionnaire is acceptable; they must avoid leading, vague, or double-barrelled questions.
Revision Plan
- 1Day 1-2: Learn definitions and examples of each sampling method (random, systematic, stratified, quota) and their pros and cons.
- 2Day 3-4: Practice stratified sampling calculations with different population sizes and strata.
- 3Day 5-6: Study questionnaire design principles and critique sample questionnaires, identifying flaws.
- 4Day 7-8: Revise data representation methods, focusing on choosing appropriate charts and interpreting them.
- 5Day 9-10: Complete past paper questions on B2b, marking your answers against mark schemes and noting common errors.
Exam Question Types
- 📋Describe how to take a stratified sample and calculate the number from each stratum. Advice: Show the sampling fraction and multiply by each stratum size.
- 📋Design a questionnaire or critique a given questionnaire, suggesting improvements. Advice: Focus on unbiased wording, clear response options, and relevance.
- 📋Interpret a chart or graph and identify any misleading features. Advice: Check axes, scales, and labels for accuracy and clarity.
- 📋Explain the advantages and disadvantages of a given sampling method. Advice: Link to bias, representativeness, and practicality.
Command Word Expectations (AQA)
Give a detailed account of the method, including steps and key features. Marks awarded for clear, sequential explanation.
Show working and give the final answer with correct units or labels. Marks awarded for correct method and accuracy.
Give reasons or justifications for a statement or method, linking to statistical concepts. Marks awarded for cause-effect reasoning.
How Students Lose Marks (Examiner Pitfalls)
Step-by-Step Worked Solutions
Question: A school has 1200 students. The numbers in each year group are: Year 7: 200, Year 8: 250, Year 9: 300, Year 10: 250, Year 11: 200. A stratified sample of 120 students is to be taken. Calculate how many students should be sampled from each year group.
- 1.Step 1: Identify the total population size (1200) and the sample size (120).
- 2.Step 2: Calculate the sampling fraction: sample size / population size = 120/1200 = 1/10.
- 3.Step 3: Multiply each year group size by the sampling fraction: Year 7: 200 × 1/10 = 20; Year 8: 250 × 1/10 = 25; Year 9: 300 × 1/10 = 30; Year 10: 250 × 1/10 = 25; Year 11: 200 × 1/10 = 20.
- 4.Step 4: Check that the sum equals 120: 20+25+30+25+20 = 120.
Question: A researcher wants to survey people's opinions on a new park. Describe how to take a systematic sample of 50 people from a queue of 500 people waiting outside a stadium.
- 1.Step 1: Number the people in the queue from 1 to 500.
- 2.Step 2: Calculate the sampling interval: population size / sample size = 500/50 = 10.
- 3.Step 3: Choose a random starting point between 1 and 10, e.g., 7.
- 4.Step 4: Select every 10th person after the starting point: 7, 17, 27, ..., up to 497.
- 5.Step 5: Survey those 50 selected people.