Sampling Bias Examples in Statistics

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

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

Concept Recap

Sampling bias occurs when a sample is collected in a way that systematically makes some members of the population more likely to be included than others, producing results that do not accurately represent the full population and leading to misleading conclusions.

Asking only your friends about favorite music doesn't tell you what the whole school thinks - your friends probably have similar tastes! That's bias. A good sample is like a well-shuffled deck: everyone has an equal chance of being picked.

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: A sample is biased when certain members of the population are systematically more or less likely to be included, making the sample unrepresentative.

Common stuck point: Students think bigger samples automatically fix bias. A survey of 1 million people can still be biased if it only reaches one type of person.

Sense of Study hint: When checking for sampling bias, first identify the target population you want to generalize to. Then examine how the sample was selected and ask: 'Is any group systematically excluded or over-represented?' Finally, consider whether the sampling method gives every member an equal (or known) chance of being included.

Worked Examples

Example 1

easy
A school wants to know whether students prefer longer lunch breaks. They survey students in the cafeteria at lunchtime. Identify the sampling bias.

Solution

  1. 1
    Step 1: The population of interest is all students in the school.
  2. 2
    Step 2: By surveying only students in the cafeteria, they miss students who eat elsewhere (classroom, outside, skip lunch). This is a convenience sample.
  3. 3
    Step 3: Students in the cafeteria may have stronger opinions about lunch because they actively use the lunch period, making the sample biased toward students who value lunchtime.

Answer

The sampling bias is that only students in the cafeteria are surveyed, excluding those who eat elsewhere. This convenience sample may over-represent students who care about lunch breaks.
Sampling bias occurs when some members of the population are more likely to be selected than others. Convenience sampling — surveying whoever is easiest to reach — is a common source of bias that can produce results that do not represent the whole population.

Example 2

medium
A website runs an online poll asking 'Should the government raise taxes?' and 90% of respondents say 'No'. Can this result be trusted? Explain what type of bias is present.

Practice Problems

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

Example 1

medium
A researcher wants to estimate the average income of adults in a city. She interviews people at a shopping centre on a weekday morning. Identify two sources of bias in her sampling method.

Example 2

hard
In the 1936 US presidential election, the Literary Digest magazine polled 2.4 million people and predicted Alf Landon would win. Instead, Franklin Roosevelt won in a landslide. The magazine had sampled from telephone directories and car registration lists. Explain why the poll failed despite its enormous sample size.
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Background Knowledge

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

data collectionpopulation vs sample