Edexcel GCSE Statistics

A statistical investigation is not a single calculation. It is a sequence of decisions, and the statistical enquiry cycle names the stages in the order they happen. The same stages organise the whole of GCSE Statistics: a question in any topic is usually asking about one stage, or about how two neighbouring stages depend on each other.

The five stages

1. Plan the enquiry.
2. Collect the data.
3. Process and represent the data.
4. Interpret the results.
5. Communicate the findings and evaluate the work.

The word cycle matters. The evaluation at the end usually shows something that could be done better, or a new question the results have raised, so the investigation goes round again with a refined hypothesis, a better sample or a different diagram. Conclusions in statistics are built up through repeated testing and refinement and are rarely settled by a single pass.

Planning

Planning starts with a question or a hypothesis, a statement that can be tested by collecting and analysing data. "As motorcycles get older, their value goes down" is a hypothesis. "Are motorcycles worth less when they are old?" is only a question, and it does not say what result would support or contradict it.

The plan then settles three things, each with a reason:

• which data is needed, and the way it will be gathered and written down;
• how to process the data once it is collected;
• how to represent the data so that it answers the question.

A good plan also looks ahead to the things that can go wrong: difficulty in identifying the population, people who do not reply, a cost or time limit, or a question that is too sensitive to ask directly. Deciding in advance how each will be handled is called a proactive strategy.

Collecting

The constraints on getting hold of suitable data depend on where it comes from.

• Primary data is collected by the investigator for this purpose, so the collection method has to be designed: the sample, the questions, the recording sheet.
• Secondary data already exists, in reference publications, on the internet or in the media. The investigator has to judge whether it is reliable, whether it is complete enough, and whether it covers the right population and time period. The source has to be acknowledged.
• Sensitivity can limit what is available. People may refuse to answer questions about their income, health or illegal behaviour, and organisations may not publish figures they regard as confidential.

Processing and representing

Data is organised into tables, summarised with statistical measures such as averages and measures of spread, and shown in diagrams. Technology such as spreadsheets and statistical software can do this quickly and for very large data sets, so an investigator needs to be able to read the output it produces (a chart, a table of summary statistics, a regression equation) as well as produce calculations by hand. Software also produces misleading charts as easily as good ones, so choosing the right diagram stays a human decision.

Interpreting

Results mean nothing until they are tied back to the context of the problem. This stage includes:

• describing what the diagrams and the calculated values show;
• reaching conclusions that answer the original question or hypothesis;
• making inferences about a population from a sample, or predictions for values not yet observed;
• discussing how reliable the findings are, which depends on the sample size, how the sample was chosen and how the data was collected.

A comment such as "the median is higher" is only a description. "The median is higher, so a typical value for this group is larger" is an interpretation in context.

Communicating and evaluating

Findings are written for a particular audience. A report for a technical reader can use standard deviations and regression equations; one for the general public is usually clearer with a simple chart and plain language. In either case the points should be clear, brief and in an order that follows the question.

Evaluation asks what was weak in the approach or in a representation (a small or biased sample, a misleading scale, a measure that does not suit the data), how the process or the presentation could be improved, and how the work could be refined to give a firmer answer to the original hypothesis. The refinements lead into the next turn of the cycle.