The Statistical Enquiry Cycle and Data Collection

How a statistical enquiry works

Statistics is a way of answering a question with data, and it follows a clear cycle. You plan the enquiry, collect the data, process and represent it, and then interpret and evaluate what you found. The data you gather comes in types: qualitative data describes qualities in categories, such as colour, while quantitative data is numerical, and numbers can be discrete, counted in whole steps, or continuous, measured on a scale. Data you collect yourself is primary, and data already gathered by someone else is secondary. Because you usually cannot ask everyone, you study a sample of the population, and the sample must be chosen fairly so the results are not biased. This module covers the enquiry cycle, the types of data, sampling methods, and how to write good questionnaire questions.

Statistics words

Learn what each of these means before you use it.

Qualitative against quantitative

The first thing to decide about data is whether it is described or numerical.

How to run a fair enquiry

A statistical enquiry follows a cycle, and keeping to it stops you jumping to conclusions. First plan: decide the question and how you will answer it. Then collect the data you need, choosing a sample that fairly represents the population rather than just the people nearest to hand. Next process and represent the data using calculations and charts. Finally interpret and evaluate what you found, and judge how reliable it is. Whenever you pick a sample, the aim is the same: give the whole population a fair chance to be included, so the results are not biased and the conclusions can be trusted.

Match the data type to an example

Which sampling method?

A researcher chooses a sample by picking every tenth person on a list. Which sampling method is this?

• systematic sampling, because it selects at a regular interval
• random sampling, where each person is chosen purely at random
• stratified sampling, in proportion to the subgroups
• a census, which surveys everyone

A good questionnaire question

Select the TWO features of a good questionnaire question.

• It is clear and easy to understand
• It avoids leading the respondent towards an answer
• It uses overlapping response boxes
• It asks two different things at once

Work out the sample size

A school has 500 pupils. A researcher wants a sample that is 10 per cent of the pupils. Work out how many pupils are in the sample.

Order the enquiry cycle

Put the four stages of the statistical enquiry cycle in order, from the start.

• Plan the enquiry and the question
• Collect the data
• Process and represent the data
• Interpret and evaluate the results

Complete the statistics facts

Data that describes qualities in categories, such as colour, is called _____ data. Data that is counted or measured as numbers is called _____ data. The whole group being studied is the _____, while a smaller part of it that is actually studied is a _____.

Match the sampling method

Spot the true statistics facts

Tap the TWO statements that are true.

• Primary data is data you collect yourself
• A stratified sample reflects the subgroups of the population
• Qualitative data is always a number
• A leading question makes a questionnaire more fair

Plan the investigation

Read each case and choose the best response, with a reason.

• You want every pupil in a school to have an equal chance of being picked for a survey. Which method fits?
• You are recording the shoe sizes of a class, which come in set sizes. What type of data is this?
• A questionnaire asks: do you agree that our wonderful park is the best in town? What is wrong with it?

Explain the enquiry cycle

A friend is starting GCSE Statistics and asks how a statistical investigation is carried out. Explain the statistical enquiry cycle and data collection.

• Explain the four stages of the statistical enquiry cycle
• Explain the difference between qualitative and quantitative data
• Explain the difference between primary and secondary data
• Explain what a sample is and why it should represent the population
• Finish by explaining one feature of a good questionnaire question