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.

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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: Sampling Bias starts by matching the sample and collection method to the population named in the question.

Common stuck point: Students often know a procedure related to sampling bias but skip the recognition step: Do I know the population, the sample, and the method used to choose or measure the cases? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Do I know the population, the sample, and the method used to choose or measure the cases?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Sampling Bias Mistakes

Worked Examples

Example 1

medium
A study finds 'people who eat breakfast are healthier' by surveying breakfast eaters at a gym. Identify the bias and explain how it distorts the conclusion.

Answer

Selection bias — gym attendees skew healthier\text{Selection bias — gym attendees skew healthier}

First step

1
Gym-goers are healthier on average than the general population.

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Example 2

hard
WWII analysts initially wanted to armor planes where returning planes had bullet holes. Statistician Abraham Wald argued the opposite. What bias did Wald identify?

Example 3

challenge
Design a strategy to reduce nonresponse bias in a postal survey expected to get a 20%20\% initial response.

Example 4

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

Example 5

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

easy
A radio host asks listeners to call in and vote on a city issue. Why might this sample be biased?

Example 2

easy
Surveying only people leaving a gym about national exercise habits will likely overstate activity levels. What bias is this?

Example 3

easy
A survey about phone-app usage is conducted only online. Which group is undercovered?

Example 4

easy
Does sampling bias come from the sample being too small, or from how the sample was selected?

Example 5

easy
A teacher surveys only the front-row students about class difficulty and generalizes to the class. Why is this biased?

Example 6

easy
A poll about a product is sent only to past buyers. Why might satisfaction be overstated?

Example 7

easy
Which sampling approach avoids sampling bias: convenience, voluntary response, or simple random sampling?

Example 8

easy
A street interviewer only approaches people who look friendly. What bias does this introduce?

Example 9

medium
A 1936 magazine poll predicted the wrong election winner because it sampled from car and telephone owners, who were wealthier. Name the bias and explain the mechanism.

Example 10

medium
Two surveys estimate average income. Survey A randomly samples 300 households; Survey B samples 5,000 households but only those listed in a luxury-magazine directory. Which is more trustworthy and why?

Example 11

medium
A customer-satisfaction survey gets responses mostly from very angry or very pleased customers. Name this bias and one way to reduce it.

Example 12

medium
A poll asks 'Don't you agree that the unfair new tax should be repealed?' Why does the wording create bias, and what type is it?

Example 13

medium
A school surveys students during a voluntary lunchtime club meeting to learn about all students' study habits. Identify two distinct biases at work.

Example 14

medium
A pollster randomly selects 2,000 phone numbers but 90% don't answer; the 10% who do skew older. Name the bias and explain why random selection didn't prevent it.

Example 15

medium
An online review site shows an average rating of 4.8 stars, but most buyers never leave reviews. Why might 4.8 overstate true satisfaction?

Example 16

challenge
Survey 1 finds 70% support using random digit dialing of landlines only; Survey 2 finds 55% support using a properly mixed random sample of all phone types. The true value is unknown. Explain why Survey 1's number is likely biased and in which direction you cannot be sure without more info.

Example 17

challenge
A study sampling hospital patients finds people who exercise more are sicker, contradicting common sense. Explain how a selection mechanism (who ends up in hospitals) could create this misleading association.

Example 18

challenge
To reduce bias when some groups are hard to reach, a researcher proposes sampling extra heavily from easy-to-reach groups 'to get a bigger sample.' Explain why this worsens bias and propose a better fix.

Example 19

medium
A researcher surveys 400 of 8,000 club members by random selection and 300 by grabbing whoever is nearby. Which subset is a trustworthy sample of the membership and why?

Example 20

medium
A survey reaches people only via a daytime landline. Working adults are underrepresented. Name the bias and one practical fix.

Example 21

easy
A magazine sends a survey on reading habits only to its current subscribers. What kind of bias does this introduce when trying to describe 'all adults'?

Example 22

easy
An interviewer wears a company-branded shirt and asks people whether they like the company. Why might responses be biased?

Example 23

easy
A teacher polls only students who got A's about how easy the test was. What bias is this?

Example 24

easy
Where in the polling process does sampling bias originate: in question wording, in how the sample is chosen, or in how data are analyzed?

Example 25

easy
An exit poll only surveys voters leaving early in the morning. What sampling bias does this create?

Example 26

medium
A survey on smartphone use is conducted only via SMS text. Which group is undercovered and how does this bias the smartphone-use estimate?

Example 27

medium
A survey on health asks people to report their weight. Reported weights are systematically lower than measured weights. Name the type of bias.

Example 28

medium
A pollster mails 1,0001{,}000 surveys; only 8080 are returned. Why is nonresponse bias a concern?

Example 29

medium
A question reads, 'Don't you think the government should fix the awful traffic problem?' Identify the bias and one way to fix it.

Example 30

medium
A study evaluates a tutoring program by averaging the after-grades of students whose parents signed them up. What sampling problem applies?

Example 31

medium
A national poll boasts 10,00010{,}000 respondents — but conducted only online. Why can it still be biased relative to 'all adults'?

Example 32

medium
A college dining survey is posted on the college's noon-only lunch line. Identify two distinct biases that could result.

Example 33

hard
An insurance company analyzes only claims that were paid out, then claims its product is reliable. Name the bias and explain why it inflates reliability.

Example 34

hard
Two studies estimate average daily exercise. Study A randomly samples 500500 from a national list and gets a 20%20\% response rate. Study B randomly samples 200200 with personal follow-up to a 90%90\% response rate. Which is likelier less biased?

Example 35

hard
A medical study only includes patients who completed the full 1212-month protocol. What bias might this introduce when comparing treatments?

Example 36

hard
A poll asks 'Do you support reasonable gun regulations?' Identify the type of bias and suggest a neutral rewording.

Example 37

hard
A media survey uses random-digit dialing of cell numbers but only calls between 9 AM and 5 PM on weekdays. What bias arises?

Example 38

challenge
A streaming service claims its hits 'always have great reviews,' citing average user ratings of 4.6/54.6/5 for top-watched shows. Identify the bias and explain it in one sentence.

Example 39

challenge
Berkson's paradox: among hospitalized patients, two unrelated diseases can appear negatively correlated even though they are independent in the general population. Why is this a sampling-bias phenomenon?

Example 40

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 41

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