Practice Sampling Methods in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Systematic approaches for selecting a subset of individuals from a population. The main probability methods are: simple random sample (SRS), stratified random sample, cluster sample, and systematic sample. Convenience sampling is a non-probability method that is generally biased.

You want to know the average GPA of 10,000 students. You can't ask everyone, so you pick a sample. How you pick matters enormously: grab the first 50 students you see in the cafeteria (convenience—biased), or give every student a number and use a random number generator to pick 50 (SRS—unbiased). Stratified sampling is like making sure you get proportional numbers from each grade level. Cluster sampling picks entire groups (like randomly selecting 5 classrooms and surveying everyone in them).

Example 1

medium
Describe four sampling methods: simple random, stratified, cluster, and systematic. Compare their advantages and disadvantages.

Example 2

hard
A school has 500 students: 200 freshmen, 150 sophomores, 100 juniors, 50 seniors. Design a proportionally stratified sample of 50 students.

Example 3

easy
A researcher wants to study opinions of 10,000 employees across 50 departments. She randomly selects 5 departments and surveys all employees in those departments. What sampling method is this, and what are its limitations?

Example 4

hard
A researcher randomly selects every 10th name from an alphabetical list of 1000 employees. Explain why this is systematic sampling, calculate the starting point needed, and describe a potential bias if the list is alphabetized by department.
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