Populations (Edexcel GCSE Statistics): Revision Notes
Populations
Understanding populations and samples
When we want to collect data about a group of people or things, we need to understand some key concepts that will help us do this effectively and accurately.
A population refers to everyone or everything that could possibly be involved in your investigation. This might be all the students in a school, all the people who use a local gym, or all the residents in a particular area. The population is the complete group you're interested in studying.
When collecting data, you have two main approaches: taking a census or using a sample.
A census involves gathering information from every single member of the population. This gives you complete information, but it takes much longer and costs significantly more than other methods. Think of the national census that happens every 10 years - it aims to collect information from every household in the country.
A sample, on the other hand, involves gathering data from only some members of the population. This is much quicker and cheaper than a census, but the key challenge is making sure your sample accurately represents the whole population.
Key terminology you need to know
Understanding these key terms is essential for working with populations and samples effectively in any statistical investigation.
Sampling units are the individual people or items that you're actually going to collect data from. If you're studying students' opinions about school meals, each student would be a sampling unit.
A sampling frame is like a complete list of all the members of the population that you could potentially choose from. For example, if you want to survey students about school meals, your sampling frame might be the school register containing all student names.
A representative sample is crucial for getting reliable results. This means your sample should contain all the important characteristics of the population to avoid bias. If your sample is too small or doesn't properly reflect the population, it might give you misleading results.
Pilot surveys and pre-tests are small-scale trials you can run before conducting your main data collection. A pilot survey tests your overall approach with a small sample, while a pre-test specifically tries out questionnaire questions to make sure they work properly.
Characteristics of good and poor samples
Understanding what makes a sample reliable is essential for collecting meaningful data.
Good samples have several important features:
- They're as large as practically possible, which helps ensure they represent the population well
- They're truly representative of the population, including all important characteristics
- They use a suitable sampling frame that accurately lists the population members
Poor samples can seriously undermine your research:
- They're too small to represent the population properly
- They're biassed, meaning they unfairly favour certain groups or characteristics
- They use a poor sampling frame that might be out of date, incomplete, or contain errors like people counted twice or names that shouldn't be there
Worked example: leisure centre investigation
Worked Example: Leisure Centre Investigation
The situation: The manager of a new leisure centre wants to find out what people in the local area think about the quality of the facilities.
Question (a): Write the population the manager should use.
Answer: The population should be all the people in the local area who use the leisure centre.
Why this answer works: The population isn't everyone in the local area, because the manager specifically wants to know about users of the leisure centre. The population must match exactly what you're trying to investigate.
Question (b): Describe a sampling unit.
Answer: A sampling unit would be one person who lives in the local area and uses the leisure centre.
Why this answer works: The sampling unit is one individual member of the population - a single person who fits the criteria we've identified.
Question (c): The manager asks 20 people who come to the leisure centre on Monday morning. Give two reasons why this sample is likely to be biassed.
Answer:
- The sample is not representative of all the people who use the leisure centre at different times and may include people who do not live in the local area.
- The sample is too small.
Why this approach is problematic: People who visit on Monday morning might have very different characteristics from those who visit at weekends or evenings. They might be retired people, shift workers, or people with flexible schedules - this doesn't represent the full range of leisure centre users. Additionally, 20 people is quite a small sample size for getting reliable results.
Common exam tips and traps
Watch out for these common mistakes when answering questions about populations and sampling:
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Don't confuse population with sample: The population is everyone you're interested in studying; the sample is just the people you actually collect data from.
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Be specific about your population: Make sure your population definition exactly matches what the question is asking about. Don't make it too broad or too narrow.
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Think about representativeness: Always consider whether a sample truly represents the population. Think about different groups, times of day, days of the week, or other factors that might affect your results.
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Sample size matters: Remember that larger samples are generally more reliable, but they must still be representative.
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Watch for bias sources: Look for ways that samples might be biassed - convenience sampling, time-based bias, or self-selection bias are common issues.
Key Points to Remember:
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A population includes everyone or everything you want to study, while a sample is just some members of that population
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A census collects data from everyone (complete but expensive), while sampling is quicker and cheaper but must be representative
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Good samples are large, representative, and use suitable sampling frames; poor samples are too small, biassed, or use inadequate sampling frames
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Always check that your population definition exactly matches what the investigation is trying to find out
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Bias can creep in through poor timing, inadequate sample size, or unrepresentative sampling methods - always think critically about whether a sample truly reflects the whole population