Collecting data and sampling

Maths: Analysis and Approaches · Statistics and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

The population is every member of the group you want to study. A sample is the part of it that you actually collect data from. A good sample represents the population fairly. A sample is biased if some members are more likely to be chosen than others, or if people choose themselves.

Data that are counted, such as the number of cars, are discrete. Data that are measured, such as time or mass, are continuous.

You must recognise five sampling techniques from a description and say which one is being used. You must also test whether a value is an outlier, using the quartiles and the interquartile range (IQR).

Rules to remember

Common mistake

Students mix up stratified and quota sampling. Both use subgroups, but a stratified sample is chosen at random within each subgroup and a quota sample is not.

Worked example

A company has 120 managers, 300 office staff and 480 factory workers. A stratified sample of 60 is taken. How many of each group are chosen?

  1. Total = 120 + 300 + 480 = 900, so the sampling fraction is 60 ÷ 900 = 1/15.
  2. Managers: 120 ÷ 15 = 8. Office staff: 300 ÷ 15 = 20. Factory workers: 480 ÷ 15 = 32.
  3. Check: 8 + 20 + 32 = 60.

Answer: 8 managers, 20 office staff and 32 factory workers.

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