Sampling (Edexcel GCSE Maths): Revision Notes
Sampling
What is sampling?
In statistics, we often need to collect information about large groups of people or objects. A population is the complete group that we want to study or learn about. However, studying an entire population can be impractical, so we use a sample instead.
A sample is a smaller group selected from the larger population. We collect data from this sample and then use it to make predictions and draw conclusions about the whole population.
The key relationship to understand is that we use sample data to make inferences about the entire population, making sampling a fundamental tool in statistical research.
Advantages of sampling
Using samples instead of studying entire populations offers several important benefits that make statistical research more practical and feasible:
- Cost-effective - It costs much less money to survey a sample than an entire population
- Time-saving - Collecting data from fewer people takes significantly less time
- Easier analysis - Working with smaller amounts of data makes calculations and statistical analysis much more manageable
These advantages explain why sampling is the preferred method in most statistical studies, from market research to medical trials. The efficiency gains are substantial while still maintaining statistical validity.
Random sampling
A random sample is one where every member of the population has an equal chance of being selected. This type of sampling helps ensure our results are fair and representative of the entire population.
Methods for selecting random samples
There are two main ways to create a random sample:
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Hat method - Write the names of every population member on separate pieces of paper, put them in a hat, and draw out your sample randomly
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Number method - Give each population member a unique number, then use a computer or calculator to generate random numbers to select your sample
Modern statistical software and calculators make the number method much more practical for large populations, while the hat method helps illustrate the concept of truly random selection.
Problems with sampling - bias
When samples are too small or poorly selected, the results can become biassed. This means the sample doesn't properly represent the whole population, making our predictions about the population inaccurate and potentially misleading.
Common causes of bias
- Sample too small - Not enough data points to represent the population fairly
- Non-random selection - Choosing people from only one group (like one class or age group)
- Limited representation - Missing important segments of the population
Bias is one of the most serious problems in sampling because it can lead to completely incorrect conclusions about the population. Always check for potential sources of bias when evaluating sample data.
Solutions to reduce bias
To minimise bias and improve the reliability of your sample results:
- Choose a larger sample size to get more reliable results
- Use random sampling methods to ensure fair selection
- Make sure the sample includes people from different groups within the population
Worked example - estimating population mean
Worked Example: Estimating Population Mean
Problem: Ashik surveys 5 students about weekly TV watching hours and gets: 15, 6, 22, 11, 18 hours. Estimate the mean for his school population.
Solution:
Step 1: Add all the values
Step 2: Divide by the sample size
Population estimate: 14.4 hours per week
Reliability assessment: This estimate isn't very reliable because the sample size is too small to represent the whole school population accurately.
Exam tips
When working with sampling problems in exams, keep these key points in mind:
- When commenting on sample reliability, always mention sample size - small samples are less reliable
- To improve reliability, suggest using a larger, random sample from the whole population
- Remember that we use sample data to make estimates about the population, not exact statements
- Look out for bias in how samples were selected - this affects reliability
Exam questions often ask you to comment on the reliability of sampling methods. Always consider both sample size and selection method in your answer.
Summary
Key Points to Remember:
- A population is the entire group being studied, while a sample is a smaller group chosen from it
- Random sampling gives every population member an equal chance of selection
- Small samples often produce biassed results that don't represent the population well
- Sampling is cheaper, quicker, and easier than studying whole populations
- To improve reliability, use larger, randomly selected samples