C2 — AQA GCSE Statistics
Test yourself on C2 with AQA GCSE practice questions.
Start free
7 days Premium · Then free forever · No card, no charge
Your focus
- Represent data sets graphically using calculated key values as necessary, and interpret and compare data sets displayed graphically as:
C2 exam tips
Quick Revision Summary (Key Takeaway)
C2 in AQA GCSE Statistics covers the collection, organisation, and representation of data, including sampling methods, data types, and graphical techniques. It is a foundational topic that underpins all statistical analysis, requiring students to understand how to gather reliable data and present it clearly.
Topic Overview
C2 focuses on the initial stages of the statistical enquiry cycle: specifying the problem, planning data collection, and processing and representing data. You will learn about different types of data (primary/secondary, quantitative/qualitative) and the strengths and weaknesses of various sampling methods, including simple random, systematic, stratified, and quota sampling. Understanding these concepts is crucial because the quality of your data collection directly affects the validity of any conclusions you draw later.
This topic also covers how to organise and present data effectively using tables, charts, and graphs such as bar charts, histograms, pie charts, and scatter diagrams. You will need to interpret these representations and identify misleading graphs. C2 provides the essential toolkit for the rest of the GCSE Statistics course, as all subsequent analysis, from calculating averages to testing hypotheses, relies on well-collected and well-presented data.
Key Concepts
- →Types of data: Primary vs secondary, quantitative vs qualitative, discrete vs continuous.
- →Sampling methods: Simple random, systematic, stratified, quota, and opportunity sampling, including advantages and disadvantages.
- →Data representation: Bar charts, pie charts, histograms (with unequal class widths), stem-and-leaf diagrams, and scatter diagrams.
- →Measures of location and spread: Mean, median, mode, range, quartiles, and interquartile range (though these are often covered in C3, basic understanding is needed here).
- →Misleading graphs: How axes scales, truncated axes, and 3D effects can distort data.
Examiner Tips
- 💡When asked to 'describe' a sampling method, write a clear step-by-step procedure. Use bullet points or numbered steps to make it easy for the examiner to award marks.
- 💡For questions on advantages and disadvantages, always relate your answer to the context. For example, 'A disadvantage of using secondary data is that it may not be up-to-date, so the conclusion about current car sales could be inaccurate.'
- 💡In graph interpretation questions, check the axes carefully. Look at the scale, units, and whether the axis starts at zero. Misleading graphs often have a broken axis or inconsistent intervals.
Common Mistakes
- Students often think that a simple random sample means 'any random sample' but it must be selected in a way that every member has an equal chance. For example, picking names out of a hat without replacement is simple random, but asking the first 10 people who walk in is opportunity sampling.
- Confusing histograms with bar charts: Histograms have no gaps between bars and the area of each bar represents frequency, not the height. Bar charts have gaps and height represents frequency.
- Believing that a larger sample is always better: A large sample can still be biased if the sampling method is flawed. Representativeness is more important than size alone.
Revision Plan
- 1Day 1-2: Learn definitions of data types and sampling methods. Create flashcards with the method name, description, advantages, and disadvantages.
- 2Day 3-4: Practice describing sampling methods in context. Use past paper questions and mark schemes to refine your answers.
- 3Day 5-6: Revise data representation. Draw each type of chart (bar chart, pie chart, histogram, scatter diagram) from given data. Focus on labelling axes and choosing appropriate scales.
- 4Day 7-8: Work through exam-style questions on interpreting graphs and identifying misleading representations. Check your answers against mark schemes.
- 5Day 9-10: Complete a full past paper section on C2 under timed conditions. Review mistakes and revisit weak areas.
Exam Question Types
- 📋Describe how to take a sample: e.g., 'Describe how to take a stratified sample of 60 students from a school.' Advice: Give clear steps, including how to select individuals within each stratum.
- 📋Identify advantages/disadvantages of data collection methods: e.g., 'Give one advantage and one disadvantage of using secondary data.' Advice: Link to context and be specific.
- 📋Interpret a graph or chart: e.g., 'Describe the trend shown in the scatter graph.' Advice: Comment on correlation, outliers, and strength of relationship.
- 📋Draw a graph: e.g., 'Draw a bar chart to represent the data.' Advice: Label axes, use a suitable scale, and ensure bars are correct height and width.
Command Word Expectations (AQA)
Describe
Give a detailed account of the method or process. For sampling, include steps such as numbering the population, using random numbers, and selecting individuals. For graphs, state what you see (e.g., 'positive correlation').
Explain
Give reasons for something. For example, 'Explain why a stratified sample might be better than a simple random sample.' You must state a reason and develop it, e.g., 'It ensures representation of all subgroups, so the sample is more representative of the population.'
Calculate
Work out a numerical answer. Show your working clearly. For example, calculating the number needed from each stratum in a stratified sample.
How Students Lose Marks (Examiner Pitfalls)
Pitfall: Students often confuse 'primary data' with 'secondary data' and fail to give a specific advantage or disadvantage in context.
❌ Weak Answer (Loses Marks):Primary data is data you collect yourself. Secondary data is data someone else collected.
Example improved answer:Primary data is collected first-hand by the researcher for the specific purpose of the investigation, whereas secondary data is collected by someone else for a different purpose. An advantage of primary data is that the researcher has control over the method and accuracy, but it can be time-consuming and expensive. Secondary data is quicker and cheaper to obtain but may be outdated or not exactly suited to the investigation.
Examiner Tip: Always link the advantage or disadvantage to the specific context given in the question. Avoid generic statements like 'it takes time' without explaining why that matters for the study.
Pitfall: When describing a sampling method, students often name it but do not explain how to carry it out, losing method marks.
❌ Weak Answer (Loses Marks):A simple random sample is when everyone has an equal chance of being chosen.
Example improved answer:To take a simple random sample, first assign each member of the population a unique number. Then use a random number generator or random number table to select the required number of unique numbers. The individuals corresponding to these numbers form the sample. This ensures every member of the population has an equal chance of being selected.
Examiner Tip: For 'describe' questions, give a step-by-step method. Use command words like 'assign', 'generate', 'select' to show the process clearly.
Step-by-Step Worked Solutions
Question: A researcher wants to sample 50 students from a school of 800. Describe how to take a stratified sample by year group. The school has 200 Year 10 students and 600 Year 11 students.
- 1.Step 1: Identify the strata (year groups) and their sizes: Year 10 = 200, Year 11 = 600.
- 2.Step 2: Calculate the proportion of each stratum in the population: Year 10 proportion = 200/800 = 0.25; Year 11 proportion = 600/800 = 0.75.
- 3.Step 3: Multiply each proportion by the sample size (50) to find the number from each stratum: Year 10 = 0.25 * 50 = 12.5 (round to 13); Year 11 = 0.75 * 50 = 37.5 (round to 37). Ensure total is 50.
- 4.Step 4: Within each year group, take a simple random sample of the required size (e.g., 13 from Year 10 and 37 from Year 11) using random numbers.
Final Answer: Take 13 students from Year 10 and 37 students from Year 11, selected randomly within each group.
Question: The table shows the number of cars sold by a dealership over 5 months: Jan 20, Feb 35, Mar 25, Apr 40, May 30. Draw a bar chart to represent this data and describe the trend.
- 1.Step 1: Label the horizontal axis with the months (Jan, Feb, Mar, Apr, May) and the vertical axis with frequency (number of cars).
- 2.Step 2: Choose a suitable scale for the vertical axis (e.g., 1 cm = 5 cars) and draw bars of equal width with gaps between them.
- 3.Step 3: Draw bars to the correct heights: Jan 20, Feb 35, Mar 25, Apr 40, May 30.
- 4.Step 4: Describe the trend: Sales fluctuate, peaking in April (40 cars) and lowest in January (20 cars). Overall, there is a slight upward trend from January to April, then a decrease in May.
Final Answer: A correctly drawn bar chart with labelled axes and bars at correct heights. The trend shows an overall increase from January to April, followed by a drop in May.
Active Recall Memory Test
What is the difference between primary and secondary data?
Key Fact: Primary data is collected first-hand by the researcher for the specific investigation. Secondary data is collected by someone else for a different purpose.
Name three sampling methods and give one advantage of each.
Key Fact: Simple random: unbiased, every member has equal chance. Systematic: easy to implement, covers the population evenly. Stratified: ensures representation of subgroups, more precise.
What is a histogram and how does it differ from a bar chart?
Key Fact: A histogram represents continuous data with no gaps between bars, and the area of each bar is proportional to frequency. A bar chart represents discrete data with gaps between bars, and height represents frequency.
What is a misleading graph and how can it be identified?
Key Fact: A misleading graph distorts the data to create a false impression. It can be identified by checking for truncated axes (not starting at zero), inconsistent scales, or 3D effects that exaggerate differences.
Frequently Asked Questions
What is the difference between stratified sampling and quota sampling?
Stratified sampling involves dividing the population into strata (e.g., year groups) and then taking a random sample from each stratum proportional to its size. Quota sampling also divides the population into groups, but the researcher selects individuals non-randomly until a quota is met. Stratified sampling is random and more representative, while quota sampling is quicker but can be biased.
How do I calculate the angles for a pie chart?
To calculate the angle for each category, divide the frequency of that category by the total frequency, then multiply by 360 degrees. For example, if a category has 10 out of 40, the angle is (10/40)*360 = 90 degrees. Always check that the sum of all angles is 360 degrees.
What are the advantages of using secondary data?
Secondary data is often quicker and cheaper to obtain than primary data, as it has already been collected. It can also provide access to large datasets that would be impractical to collect yourself, such as government statistics. However, it may be outdated or not exactly suited to your investigation.
How do I know when to use a histogram instead of a bar chart?
Use a histogram when the data is continuous and grouped into intervals (e.g., heights, times). Histograms have no gaps between bars and the area represents frequency. Use a bar chart for discrete or categorical data (e.g., favourite colours, number of siblings), where bars have gaps and height represents frequency.
What is opportunity sampling and why is it often biased?
Opportunity sampling (or convenience sampling) involves selecting individuals who are easily available at the time, such as asking the first 20 people who walk past. It is often biased because the sample may not be representative of the whole population; for example, it might over-represent a particular age group or location.
How can I avoid losing marks on sampling method questions?
Always read the question carefully and ensure you describe the method step-by-step. Use key terms like 'random number generator', 'strata', 'quota', and 'systematic'. For advantages and disadvantages, link them to the context of the investigation. Practice with past paper mark schemes to see exactly what examiners expect.