The Statistical Enquiry Cycle: Reviewing the Whole Investigation
This lesson covers the general principles of the Statistical Enquiry Cycle that apply to all students. The specific investigation, data and methods your class used in a class project or practical investigation will be different — refer to your teacher’s notes alongside this lesson.
The Statistical Enquiry Cycle: Five Stages
Every technique you have learned so far — sampling methods, charts, averages, correlation — fits inside one overarching framework called the Statistical Enquiry Cycle. This cycle links planning, collecting, processing, interpreting and communicating an investigation into a single connected process. Both of your exam papers contain short, medium and extended response questions, and questions can draw on the component parts of the Statistical Enquiry Cycle rather than one technique in isolation.
The five stages of the cycle are:
- Stage 1 — Planning: define a question or hypothesis to investigate, decide what data to collect and how to collect and record it, and develop a strategy for processing and representing that data — giving reasons for each choice.
- Stage 2 — Sourcing Data: recognise the constraints involved in finding appropriate data, whether collecting primary data yourself or researching secondary sources, and acknowledge where sensitive topics may limit what data is available.
- Stage 3 — Processing and Presenting Data: organise and clean the data, generate diagrams and visualisations, and calculate statistical measures to compare data sets.
- Stage 4 — Interpreting Results: analyse the diagrams and calculations, reach conclusions that relate back to the original question, make inferences or predictions, and discuss how reliable the findings are.
- Stage 5 — Communicating Findings and Evaluating: present conclusions clearly for the intended audience, identify weaknesses in the approach or representation, and suggest improvements that would refine the investigation.
The five stages are Planning, Sourcing Data, Processing and Presenting Data, Interpreting Results, and Communicating Findings and Evaluating. Extended response questions can draw on more than one of these stages at once.
Stage 1 in Detail: Planning and Proactive Strategies
A hypothesis can only be tested through the appropriate collection and analysis of data — for example, the hypothesis ‘as motorcycles get older, their value is likely to go down’ can be tested by collecting age and price data for a sample of motorcycles. A vague hypothesis with no measurable variables cannot be tested properly, so defining it precisely is the first job of Stage 1.
Good planning also means thinking ahead about what could go wrong before data collection even begins. This is what the specification calls determining proactive strategies — for example, deciding in advance how you will handle a low response rate to a questionnaire, how you will identify your population if it is not obvious, or what you will do if the results come out completely unexpected.
Stage 2 in Detail: Sourcing Data
Before data can be processed, it has to be sourced. Primary data (data you collect yourself) comes with constraints such as cost, time and ethical issues. Secondary data (data collected by someone else, from places such as government publications, the internet or the media) must always have its source acknowledged, so a reader can judge how reliable it is. Some topics — such as income, health or personal habits — are sensitive, and this can restrict what data is available or how honestly people respond.
Stage 3 in Detail: Processing and Presenting Data
Once the data is in, it has to be made usable. Cleaning comes first: removing or correcting values that are impossible, duplicated or in the wrong units, and deciding what to do about gaps. Then the data is organised, usually into a frequency table or a grouped table, so that it can be summarised.
Presenting means choosing a diagram that suits the type of data: a bar chart or pie chart for categories, a histogram or cumulative frequency curve for grouped continuous data, a scatter diagram for two variables, a time series graph for data collected over time. Processing means calculating the measures that let you compare data sets, such as the mean, median, quartiles, interquartile range and standard deviation. The exam board expects you to justify the format you chose and to spot when a diagram misleads. The techniques themselves are practised in the Representing and Processing Data and Numerical Measures units; this lesson is about knowing where they sit in the cycle.
Stage 4 in Detail: Interpreting Results in Context
Interpretation is where the numbers turn into meaning. It is not enough to calculate a mean or draw a scatter diagram — you must analyse what it shows, and relate your conclusion back to the original hypothesis. A weak conclusion says ‘the mean is higher.’ A strong conclusion says ‘students who revised for more than five hours scored higher on average, with a mean of 72% compared with 58% for those who revised for under two hours’ — a specific, contextual statement that answers the original question.
Reliability of findings depends on several things: how large and representative the sample was, whether the data collection method was valid, and whether another explanation could account for the pattern. Always ask: could a different, unmeasured factor explain this result just as well?
Justifying Format and Avoiding Graphical Misrepresentation
Choosing a graph is not just about what looks tidy — you must be able to justify why a particular format suits the data and the audience. A scatter diagram suits bivariate data because it shows the relationship between two variables; a histogram suits grouped continuous data because it shows the shape of a distribution. Producing the correct diagram, and being able to explain why it was chosen over an alternative, is assessed directly.
Graphs can also mislead, even when the underlying data is correct. Common construction errors include incorrect scales, a truncated axis that does not start at zero, and distorted sizing in diagrams such as pictograms or 3D charts. Recognising these errors — and explaining exactly how they distort the reader’s impression of the data — is part of the specification content on misleading and misrepresentative diagrams.
A bar chart comparing two shops’ weekly sales might use a vertical axis that starts at £40,000 instead of £0. If Shop A sold £42,000 and Shop B sold £45,000, the bars will look wildly different in height, even though the real difference is only about 7%. The axis has exaggerated a small difference into what looks like a huge one.
Pictograms cause a similar problem when the symbols themselves change size rather than number — a bigger symbol can look like it represents far more than the key states, misleading anyone who judges area rather than reading the key. Always check: does the scale start at zero, and does every symbol represent the same fixed amount?
For unequal-width histograms, frequency density (frequency ÷ class width) must be plotted on the vertical axis rather than raw frequency — plotting raw frequency produces a diagram whose bar heights give a false impression of the distribution.
Stage 5 in Detail: Communicating Findings and Evaluating
Stage 5 combines two skills: communicating clearly, and evaluating honestly. Communication means presenting your findings so that your target audience can understand them — a report for a school newsletter needs simpler language and fewer technical terms than one written for a statistics teacher, even if the underlying statistics are identical.
Evaluating means identifying specific weaknesses in your approach or representation, and suggesting concrete improvements — not simply saying the investigation ‘could have been better.’ A strong evaluation point names the weakness, explains why it undermines the conclusion, and proposes a specific fix.
This question presents a fictional investigation and asks you to critique it across the cycle. Step 1: identify a weakness at a named stage — for example, at the Sourcing Data stage: ‘the investigator used opportunity sampling from one shopping centre.’
Step 2: explain why this weakness undermines the conclusion: ‘This means the sample is likely biased towards shoppers at that location, who may differ from the wider population in their habits, so the conclusion cannot be generalised.’
Step 3: suggest a specific improvement: ‘A stratified random sample drawn from a complete sample frame of the target population would reduce this bias.’
Step 4: repeat the same three-part structure for a weakness at a second, different stage of the cycle — for example, a vague hypothesis identified at the Planning stage. Responses that only describe what the investigator did, without explaining why it is a problem, cannot reach the top mark band.
Sample Size, Reliability and Replication
The specification makes a direct point about sample size: results are generally more reliable, and more likely to replicate, when they are based on a larger sample. Replication matters because a one-off result could just be a coincidence of who happened to be sampled.
A small sample lets one or two unusual respondents dominate the results — a single outlier in a sample of 10 has far more influence than a single outlier in a sample of 1,000. This is why increasing the sample size is a useful improvement to suggest — but only when it is linked to a specific weakness rather than offered as a generic fix.
Full-mark evaluation: (1) identify the weakness at a named stage of the cycle, (2) explain why it undermines the conclusion, (3) suggest a specific, actionable improvement. Repeat this structure at a second, different stage for the top mark band.
Describing says: ‘the investigator used opportunity sampling.’ Evaluating says: ‘the use of opportunity sampling means the sample over-represents people who happened to be in that location, which may not reflect the wider population, so the conclusion cannot be generalised with confidence.’
Every strong evaluation point has all three parts — weakness, impact, fix. An answer that omits the impact or the improvement is describing rather than evaluating, and will earn fewer marks even if the statistics elsewhere in the answer are flawless.