Sampling methods and bias worksheet for Statistics
A stratified sample takes some from every group; a cluster sample takes every member of a few groups. Convenience and voluntary response samples are not random at all, which is where most bias starts.
Also taught in Algebra 2, at its own level and with its own examples.
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Name the sampling method, and say whether it is random and why. A city randomly chooses 9 of its 80 neighborhoods and surveys every household in the chosen neighborhoods.
Name the sampling method, and say whether it is random and why. A highway officer picks one of the first 25 cars at random, then checks the speed of every 25th car that passes.
Name the sampling method, and say whether it is random and why. A graduate student surveys the people sitting near her in the library.
Name the sampling method, and say whether it is random and why. A city gives a number to each registered voter and uses a random number generator to choose 350 to call.
Name the sampling method, and say whether it is random and why. A company randomly selects 16 employees from each of its five departments.
Name the sampling method, and say whether it is random and why. A magazine prints a survey and tallies the replies of readers who choose to mail it back.
Name the sampling method, and say whether it is random and why. An apartment company randomly chooses 6 of its 24 buildings and surveys every tenant in those buildings.
Name the sampling method, and say whether it is random and why. A mall worker surveys the first 35 shoppers who walk by.
Name the sampling method, and say whether it is random and why. A farmer picks a random tree among the first 8 in an orchard row, then inspects every 8th tree after it.
Name the sampling method, and say whether it is random and why. A factory picks one of the first 140 phones off the line at random, then tests that phone and every 140th phone after it.
Name the bias
Name the bias and explain it. A school posts a link about a later start time and counts the votes of parents who choose to click it.
Name the bias and explain it. A survey asks, “Don't you agree that cruel animal testing should be banned?”
Name the bias and explain it. Students are asked in front of their teacher whether they have ever cheated.
Name the bias and explain it. A survey on how people plan to vote uses only the list of people who voted in the last election.
Name the bias and explain it. A hotel leaves a survey in the rooms of 250 randomly chosen guests, and only 24 respond.
Name the bias and explain it. A store asks only customers on its email list about its prices.
Name the bias and explain it. A college emails a survey to 2,000 randomly chosen graduates, and only 180 respond.
Name the bias and explain it. A college asks only students who live on campus about parking needs.
Name the bias and explain it. A city picks 500 residents at random for a survey, but even after three reminders only 30 respond.
Name the bias and explain it. A website posts a poll on a new gun law and counts the visitors who choose to vote.
Name the sampling method, and say whether it is random and why. A city randomly chooses 9 of its 80 neighborhoods and surveys every household in the chosen neighborhoods.Cluster sample; random: the groups are chosen at random
Name the sampling method, and say whether it is random and why. A highway officer picks one of the first 25 cars at random, then checks the speed of every 25th car that passes.Systematic sample; random: the starting point is chosen at random
Name the sampling method, and say whether it is random and why. A graduate student surveys the people sitting near her in the library.Convenience sample; not random: the sampler takes whoever is easiest to reach
Name the sampling method, and say whether it is random and why. A city gives a number to each registered voter and uses a random number generator to choose 350 to call.Simple random sample; random: chance alone picks the sample, and every group of that size is equally likely
Name the sampling method, and say whether it is random and why. A company randomly selects 16 employees from each of its five departments.Stratified random sample; random: members are chosen at random within each group
Name the sampling method, and say whether it is random and why. A magazine prints a survey and tallies the replies of readers who choose to mail it back.Voluntary response sample; not random: people choose themselves
Name the sampling method, and say whether it is random and why. An apartment company randomly chooses 6 of its 24 buildings and surveys every tenant in those buildings.Cluster sample; random: the groups are chosen at random
Name the sampling method, and say whether it is random and why. A mall worker surveys the first 35 shoppers who walk by.Convenience sample; not random: the sampler takes whoever is easiest to reach
Name the sampling method, and say whether it is random and why. A farmer picks a random tree among the first 8 in an orchard row, then inspects every 8th tree after it.Systematic sample; random: the starting point is chosen at random
Name the sampling method, and say whether it is random and why. A factory picks one of the first 140 phones off the line at random, then tests that phone and every 140th phone after it.Systematic sample; random: the starting point is chosen at random
Name the bias
Name the bias and explain it. A school posts a link about a later start time and counts the votes of parents who choose to click it.Voluntary response bias: people with strong opinions answer
Name the bias and explain it. A survey asks, “Don't you agree that cruel animal testing should be banned?”Response bias: the question is worded to lead
Name the bias and explain it. Students are asked in front of their teacher whether they have ever cheated.Response bias: people do not answer honestly
Name the bias and explain it. A survey on how people plan to vote uses only the list of people who voted in the last election.Undercoverage: new and first-time voters are left out
Name the bias and explain it. A hotel leaves a survey in the rooms of 250 randomly chosen guests, and only 24 respond.Nonresponse bias: most of the sample did not respond, and those who do not respond may differ from those who do
Name the bias and explain it. A store asks only customers on its email list about its prices.Undercoverage: customers not on the email list are left out
Name the bias and explain it. A college emails a survey to 2,000 randomly chosen graduates, and only 180 respond.Nonresponse bias: most of the sample did not respond, and those who do not respond may differ from those who do
Name the bias and explain it. A college asks only students who live on campus about parking needs.Undercoverage: students who commute are left out
Name the bias and explain it. A city picks 500 residents at random for a survey, but even after three reminders only 30 respond.Nonresponse bias: most of the sample did not respond, and those who do not respond may differ from those who do
Name the bias and explain it. A website posts a poll on a new gun law and counts the visitors who choose to vote.Voluntary response bias: people with strong opinions answer
A city randomly chooses 8 of its 60 neighborhoods and surveys every household in those 8.
The city picks whole groups at random.
Then it surveys everyone inside the groups it picked.
The answer is Cluster sample.
Where students go wrong
Mixing up stratified and cluster. Stratified: a few from every group. Cluster: all from a few groups.
Also called types of sampling, stratified vs cluster, sampling bias or survey bias.
What you can put on this worksheet
Name the sampling method
Name the sampling method. An apartment company randomly chooses 5 of its 21 buildings and surveys every tenant in those buildings.→ Cluster sample
Name the bias
Name the bias. A coach asks players, in front of the whole team, whether they skipped any workouts.→ Response bias
Questions about these worksheets
Yes. Every sampling methods and bias sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the sampling methods and bias questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: name the sampling method and name the bias. Tick as many as you want and set how many of each, or let it spread them evenly.
Mixing up stratified and cluster. Stratified: a few from every group. Cluster: all from a few groups.