Practice Sampling Bias in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Sampling bias occurs when the method of selecting a sample systematically over- or under-represents certain groups relative to their actual proportion in the population.
A biased sample gives you a skewed picture of the population — like judging average student height by only surveying the basketball team.
Showing a random 20 of 50 problems.
Example 1
easyWhich sampling method best avoids bias: (a) ask friends, (b) random selection from a full population list?
Example 2
easyA website asks 'Do you love our product?' with only a 'Yes' button. What bias does this design create?
Example 3
mediumAn online poll about smartphone usage is biased. Why?
Example 4
mediumAn online opt-in poll says '70% oppose the policy.' Why can't we trust this as the national figure?
Example 5
easyA study of national TV-watching habits surveys only people on a streaming-only platform. Bias?
Example 6
easyA reporter interviews people only outside one coffee shop. What type of bias is most likely?
Example 7
mediumA survey of grocery shoppers about prices is conducted only at premium organic stores. Bias?
Example 8
easyFill in the blank: a sampling method that systematically over- or under-represents some groups produces ___ bias.
Example 9
mediumWhy is a survey conducted at the food court at am likely biased for estimating teenager opinions?
Example 10
mediumA city has 60% renters and 40% owners, but a survey of 500 reaches 90% owners. The estimate of 'support for rent control' will likely be biased in which direction, given owners oppose it?
Example 11
mediumResearchers sample households by knocking on doors only at houses with cars in the driveway. Who is excluded?
Example 12
mediumA radio show asks listeners to call in about gun control. What two biases dominate?
Example 13
mediumA company emails customers a satisfaction survey; respond. What bias is likely?
Example 14
mediumA pollster asks 'Don't you agree that taxes are too high?'. What bias is this?
Example 15
mediumA magazine surveys its readers about political preferences and finds 75% support Policy X. Explain why this result may not represent the general population, identifying the bias type.
Example 16
mediumIf true support is 50% but a method always over-counts supporters by reaching them more often, the estimate's expected value is above 50%. Is this bias or random error?
Example 17
hardAn online survey about internet usage gets 10,000 responses. Explain why this large sample does not eliminate bias, and identify what type of people are systematically excluded.
Example 18
challengeTwo designs: A has bias , SE ; B has bias , SE . Using total error , which is more accurate?
Example 19
hardA medical trial uses only volunteers. Why might results not generalize to the patient population?
Example 20
challengeA survey reaches group X with probability and group Y with . X favors a measure 20%, Y favors 80%, and the population is half X, half Y. Find the true rate and the (unweighted) sampled rate.