Populations, censuses and samples

Key words

• Population: the whole set of items of interest.
• Census: a survey of every member of the population.
• Sample: a selection of members of the population, used to find out about the whole population.
• Sampling unit: an individual member of the population that can be sampled.
• Sampling frame: a list of all the sampling units (for example, a list of all students on a school roll, with ID numbers).

Census

Advantages: every member is included, so the result is unbiased and gives a full, accurate picture.

Disadvantages: it takes a long time and is expensive; it can be hard to make sure every member is surveyed; there is a lot of data to process; and it is impossible when testing destroys the item (for example, the lifetime of light bulbs).

Sample

Advantages: cheaper and quicker; less data to process; the only option when testing is destructive; it may be the only practical option for a very large population.

Disadvantages: the results are subject to natural variation between samples (uncertainty), and the sample may be biased, so it may not represent the population.

Worked example

A factory wants to know the mean lifetime of the bulbs it makes. Explain why it should use a sample, and suggest a sampling frame.

1. Testing a bulb's lifetime destroys it, so a census would leave nothing to sell.
2. A sampling frame could be a list of the serial numbers of the bulbs made that day.

Answer: A sample, because testing is destructive; frame: a list of serial numbers of all bulbs produced.

Check yourself

1. Which is a sampling frame for a survey of members of a sports club?
   • One member of the club
   • The 50 members who answer the survey
   • The club's list of all its members
   • All the members of the club
   Show answer

   The club's list of all its members. A sampling frame is a list of sampling units.

2. In a survey of the trees in a forest, what is the sampling unit?
   • A single tree
   • All the trees in the forest
   • A map of the forest
   • The trees chosen for the survey
   Show answer

   A single tree. The sampling unit is an individual member that can be sampled.

3. Why would a census be unsuitable for testing the breaking strength of all the ropes a company makes?
   • It would give biased results
   • Ropes cannot be listed
   • Testing breaks the ropes, so none would be left to sell
   • A census gives less accurate results than a sample
   Show answer

   Testing breaks the ropes, so none would be left to sell. Destructive testing rules out a census.

4. Which is an advantage of a census over a sample?
   • It is quicker
   • It gives an unbiased, complete picture of the population
   • It is cheaper
   • There is less data to process
   Show answer

   It gives an unbiased, complete picture of the population. Every member is included.

5. Which is a disadvantage of using a sample?
   • It always costs more than a census
   • It can never be used for large populations
   • It needs every member of the population to be surveyed
   • Natural variation means different samples give different results
   Show answer

   Natural variation means different samples give different results. Sample results are uncertain because samples vary.

6. A teacher asks every one of her 28 students about their homework time. What is this?
   • A sample
   • A census
   • A sampling frame
   • A sampling unit
   Show answer

   A census. Every member of the population (her class) is asked.

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Sources

• Pearson Edexcel International Advanced Level in Mathematics specification (issue 3), Unit S2

Last updated 8 November 2026. Spotted a mistake? Tell us.