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Background reading · Mathematics and Statistics

Data detectives: how statisticians investigate

The PPDAC cycle (Problem, Plan, Data, Analysis, Conclusion) is how statisticians turn a question into an answer they can trust.

Every few years, Stats NZ asks every person in the country the same set of questions in the census. The answers help decide where new schools, hospitals and bus routes go. Statisticians in New Zealand, and students in CensusAtSchool, use the same five-step cycle to investigate. It is called PPDAC.

The five steps

  • Problem: ask a statistical question, one where you expect the answers to vary. 'How long did I sleep last night?' has one answer. 'How long do students in our class usually sleep on a school night?' has many, and the variation is the interesting part. Predict the answer before you collect anything.
  • Plan: decide who or what you will measure, how many, and exactly how. If half the class counts sleep from lights-out and half from getting into bed, the data is ruined before you start. Test your survey question on two people first.
  • Data: collect the data and record everything, even odd values. Then clean it: look for impossible values and typing mistakes, and write down what you did about each one.
  • Analysis: draw a graph and look for the shape, the middle and the spread. Calculate the mean, median, mode and range. Look for outliers and for differences between groups.
  • Conclusion: answer your question in context, using numbers: 'The median sleep time was 9 hours 15 minutes, and most of us slept between 8 and 10 hours.' Then say how sure you are and why.

    • Limitations make it stronger

    A good conclusion always admits its limits. Was the sample big enough, and did it include everyone it should? Could the measuring have been more accurate? What new question does your answer raise?

    That last question is why PPDAC is called a cycle. A good investigation usually ends with a better question, and the next investigation starts there.

    Sources and further reading

    Written for Kōkiri Learn students in our own words. Check facts against the sources.

    Used in: What the Data Shows