Random Sampling and Bias
A free Statistics and Data Analysis lesson from the “Collecting Data” unit, with a worked example and practice problems including step-by-step solutions.
Random sampling gives every member of a population a fair chance to be selected. Bias happens when the sampling method systematically favors some outcomes over others. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Explain why random sampling matters
- Identify common sources of bias
- Connect representative samples to generalization
Worked example
Problem. A school assigns every student a number and uses a random number generator to choose 80 students for a survey. What sampling method is this?
- Every student had a fair chance to be chosen.
- That describes a simple random sample.
Answer: simple random sampling
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: A club advisor puts all member names in a digital randomizer and chooses 20 names. Which method is this?
Choices: placebo group · simple random sample · convenience sample · voluntary response sample
Show solution
- A simple random sample uses chance to choose from the whole list.
- Each member has a fair chance to be selected.
Answer: simple random sample
2. Practice case B: A study randomly chooses equal numbers from each neighborhood. Which method is this?
Choices: convenience sample · double-blind experiment · stratified random sample · cluster sample
Show solution
- The population is split into groups first.
- Then random samples are taken within each group.
Answer: stratified random sample
3. Practice case C: A researcher randomly chooses 5 classrooms and surveys every student in those classrooms. Which method is this?
Choices: simple random sample of individuals · voluntary response sample · matched-pairs experiment · cluster sample
Show solution
- Clusters are entire groups selected at random.
- Everyone in the chosen groups is included.
Answer: cluster sample
4. Practice case D: A library starts at a random shelf label and checks every 20th record. Which method is this?
Choices: systematic sample · stratified sample · voluntary response sample · placebo sample
Show solution
- Systematic sampling follows a regular interval.
- A random start helps avoid a predictable pattern.
Answer: systematic sample
5. Practice case E: A coach asks only players who arrive early to practice. What is the main concern?
Choices: the sample is too random · the sample may be a convenience sample · the result must prove causation · the variables are all quantitative
Show solution
- Convenience samples are easy to reach.
- They may not represent the whole population.
Answer: the sample may be a convenience sample
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