The Statistical Enquiry Cycle - All Five Stages

The Statistical Enquiry Cycle

Every statistics investigation, from a school survey to national research, follows the same five-stage cycle. It underpins every paper you will sit, and the order is not negotiable:

The five stages

Put the five stages of the statistical enquiry cycle into order.

• Initial planning: define the question and plan the data
• Collecting the data
• Processing and representing the data
• Interpreting the results
• Evaluating, then starting again

Out of order

A student writes their conclusion first, then goes out and gathers figures that support it. What is wrong with this?

• Interpreting comes AFTER collecting, and hunting only for data that agrees with you makes the whole enquiry biased
• Nothing, as long as the conclusion turns out to be correct
• They have skipped Stage 3, because no diagrams have been drawn yet
• You are never allowed to write anything down before collecting data

Stage 1: Initial planning

Everything starts with a clear question or hypothesis. Then you decide what data to collect and how, and plan how you will process and represent it. The examiner wants reasons for every choice: why this data, why this sampling method, why this kind of chart. "I chose a bar chart" earns nothing; "I chose a bar chart because the data is in categories" earns the mark. Planning is also where the enquiry can be sunk without anybody noticing until the end, because a badly chosen sample cannot be repaired at Stage 4.

Which stage?

A student wants to know whether pupils who walk to school arrive more alert. Writing the hypothesis and deciding to survey 30 pupils in each group is stage _____. Handing out that survey is stage _____. Working out the mean alertness score for each group and drawing a bar chart is stage _____. Saying what those figures suggest about the original question, and how far they can be trusted, is stage _____.

Stage 2: Collecting data

Data comes in two kinds, and the difference is who did the gathering and what for. Each brings its own obligations:

Whose data is it?

A student downloads a spreadsheet of last year's attendance figures from their own school office, and separately counts how many pupils are in the playground at break every day for a week. Which is which?

• The attendance figures are secondary, and the playground counts are primary
• Both are primary, because both came from the student's own school
• Both are secondary, because both are about other pupils
• The attendance figures are primary, because the student obtained them personally

Stages 3 and 4

In Stage 3, processing and representing, you organise the data, draw diagrams and calculate statistical measures such as the mean. In Stage 4, interpreting, you say what those diagrams and figures MEAN in context: you reach conclusions about the original question, make inferences, and discuss how reliable the findings are. The line between them is worth seeing clearly. "The mean was 6.8 hours" is Stage 3: it is a number you worked out. "This suggests older pupils sleep less" is Stage 4: it is a claim about the world, and it is the half most answers leave out.

Which half?

Four sentences from a student's report on sleep. Tap the TWO that belong to INTERPRETING rather than to processing.

• The mean sleep time was 6.8 hours for Year 11 and 8.1 hours for Year 7.
• This suggests that older pupils are getting less sleep, which supports the hypothesis.
• A bar chart was drawn to compare the two year groups.
• Because only 30 pupils were surveyed, the difference may not hold across the whole school.

A real enquiry

A student investigates whether Year 11 pupils sleep less than Year 7 pupils. Reason out which stage each step is in.

• First they write the hypothesis and decide to survey 30 pupils in each year. Which stage is this?
• They hand out the survey and record the pupils' answers. Which stage?
• They find Year 11s do sleep less, but only surveyed 30 pupils. What should they say about this finding?

Stage 5: Evaluating and looping

The final stage is to evaluate the whole enquiry: how reliable were the results, what were the limitations, and how could it be done better? That evaluation usually refines the question and sends you back to Stage 1 with a better one. That is precisely why this is a cycle and not a checklist: a finished enquiry is the starting point of the next one.

The loop

Stage 5 asks how _____ the results were, what the _____ of the enquiry were, and how it could be improved. That is why the whole thing is called a _____ rather than a checklist: an evaluation usually sharpens the question and sends you back to stage _____ with a better one.

Evaluate the enquiry

A student surveys 20 friends in their own tutor group and concludes that "most pupils at this school prefer online homework". Evaluate this enquiry.

• Name one problem with the way the data was collected
• Explain why that problem weakens the conclusion, rather than just naming it
• Say what the conclusion could fairly have claimed instead
• Say what you would change, and which stage of the cycle that change belongs to

Cycle summary

The statistical enquiry cycle has five stages: planning, collecting, processing and representing, _____, and evaluating. Data you collect yourself is _____ data, while data from elsewhere is _____ data and must be acknowledged. Good conclusions refer back to the original question and discuss their _____.