The Statistical Enquiry Cycle
The statistical enquiry cycle is the four-stage process statisticians follow to answer a question using data: posing a question, collecting data, processing and representing the data, and interpreting the results to reach a conclusion. It is the framework that links every other topic in GCSE Statistics together, from choosing a sample to drawing a final conclusion. Exam questions often ask you to name or describe a stage of the cycle in the context of a given scenario.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Start by posing a clear, specific statistical question or hypothesis that can be answered using data, for example comparing two groups or testing a claim.
- Plan how the data will be collected, including the population, the sampling method and what type of data is needed.
- Collect the data using a suitable method, such as a survey, experiment or existing data source.
- Process and represent the data using appropriate calculations (averages, spread) and diagrams (charts, graphs).
- Interpret the processed data to draw conclusions, and check whether the original question or hypothesis has been answered.
- Evaluate the method: consider limitations such as sample size, bias, or reliability, and suggest improvements.
Worked example
A student wants to find out whether Year 11 students at her school spend more time on homework than Year 7 students. Describe how she could apply each stage of the statistical enquiry cycle.
- Pose the question: 'Do Year 11 students spend more time on homework per week than Year 7 students?' This is a comparative question that can be tested with data.
- Plan: decide to take a random sample of, say, 30 students from each year group, and collect data on hours spent on homework per week using a questionnaire.
- Collect: distribute the questionnaire and record the number of hours reported by each of the 60 students.
- Process and represent: calculate the mean and range of hours for each year group, and draw back-to-back stem-and-leaf diagrams or box plots to compare them.
- Interpret: compare the two means and spreads to decide whether Year 11 students typically spend more time on homework.
- Final answer: the enquiry cycle is pose question, plan, collect, process/represent, interpret/conclude, with evaluation of the method throughout.
Practice questions
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Q1Which stage of the statistical enquiry cycle comes immediately after collecting the data?Show answer
Answer: Processing and representing the data
Q2Name the first stage of the statistical enquiry cycle.Show answer
Answer: Posing the question (or hypothesis)
Q3A researcher draws a bar chart from her results. Which stage of the cycle is this?Show answer
Answer: Processing and representing the data
Q4A researcher decides her sample size was too small after seeing her results. Which stage of the cycle does this belong to?Show answer
Answer: Evaluation (reviewing the method)
Q5State two things that should be decided during the planning stage of the enquiry cycle.Show answer
Answer: Any two of: the population, the sample size, the sampling method, the type of data to collect
Q6A supermarket wants to know if a new till layout reduces queuing time. Write a suitable statistical question for the start of the enquiry cycle.Show answer
Answer: For example: 'Is the average queuing time lower with the new till layout than with the old layout?'
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
State two stages of the statistical enquiry cycle, in the correct order, that come between posing the question and interpreting the results.
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A gym manager wants to know whether members who use a personal trainer lose more weight on average than members who do not. (a) Write a suitable statistical question. (b) State one thing the manager should decide at the planning stage. (c) State one way the manager could process the data once collected.
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A school council believes students who cycle to school are fitter than students who are driven. Describe, in order, the four main stages of the statistical enquiry cycle they should follow to investigate this.
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Free printable worksheet
Want more practice on paper? Download the the statistical enquiry cycle worksheet pack - 13 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 5 of GCSE Statistics Foundation Workbook 1 and chapter 5 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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