Random Sampling Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Random Sampling.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Selecting individuals from a population where every member has an equal chance of being chosen.

Drawing names from a hat where all names are equally likely to be picked. No favoritism, no convenience, just pure chance. This is how we ensure the sample represents the whole population, not just the easy-to-reach people.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Random sampling ensures every member of the population has an equal chance of selection, removing systematic bias and making the sample representative.

Common stuck point: Students think 'random' means arbitrary or haphazard. True random sampling requires a formal process — just picking whoever is convenient is not random.

Worked Examples

Example 1

easy
A school has 500 students numbered 001–500. Describe how to select a simple random sample of 20 students using a random number generator.

Solution

  1. 1
    Step 1: Assign each student a unique number from 001 to 500.
  2. 2
    Step 2: Use a random number generator to produce numbers between 1 and 500. If a number is repeated, skip it and generate another.
  3. 3
    Step 3: Continue until 20 unique numbers are selected. The students with those numbers form the sample.

Answer

Number all students 001–500, use a random number generator to select 20 unique numbers, and survey the corresponding students.
Simple random sampling gives every member of the population an equal chance of being selected. Using a random number generator eliminates human bias in the selection process and produces a representative sample.

Example 2

medium
Explain the difference between simple random sampling, stratified sampling, and systematic sampling. Give an example scenario where stratified sampling would be preferred.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A factory produces 10,000 widgets per day. A quality inspector wants to check 100 widgets. She takes every 100th widget off the production line, starting with widget number 37 (chosen randomly). What type of sampling is this? What potential problem could arise?

Example 2

hard
A university has 12,000 students: 7,200 undergraduates and 4,800 postgraduates. A researcher wants a stratified sample of 200 students. (a) How many undergraduates and postgraduates should be in the sample? (b) How does this compare to what might happen with a simple random sample?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

sampling biaspopulation vs sample