Algebra 1 · Unit 10
Choose a sampling method that represents a larger group, including random sampling, and spot biased plans.
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A sample represents a larger group
You rarely measure everyone. A good sample looks like the population you want to describe.
Random sampling
Every person or unit in the population has a chance to be chosen. A random number list, names from a hat, or a calculator’s random integer can work.
Biased methods
Asking only your friends, only people who volunteer, or only people at one lunch table can miss whole groups.
Match the population
If the question is about all 9th graders, do not sample only the soccer team.
Name the method: random, convenience, or volunteer.
Convenience sample (friends, nearby).
Friends may study more or less than the whole grade.
Answer: convenience; not representative
Simple random sample of 30 from the grade.
Answer: random
People who volunteer and who notice the poster — often more interested or more online.
Answer: volunteers
If you already have every student’s score, that is a census of the class, not a sample.
Answer: census of the class
Starters are usually faster. The sample misses the rest of the roster.
Answer: not the whole team
Every 10th name is a systematic sample from the whole list. Front row is convenience.
Answer: every 10th name
Choose a method that matches the population.
Number every student, use a random integer generator to pick 40 numbers.
One advisory may be all 9th graders, or all band kids, so it is a cluster that may not match the school.
Answer: random from the whole school
Put 200 names in a list numbered 1–200. Generate 20 distinct random integers from 1 to 200.
Answer: 20 random IDs from 1 to 200
People who did not buy. The sample is truncated toward customers.
Answer: non-buyers missing
Size does not fix a one-sided net. 500 friends of one person can still look alike.
Answer: bias ≠ small n
Randomly choose days of the week as well as people, or sample across several weekdays.
Answer: include more days
The unit is a locker. Some students have two lockers or none. You are describing lockers, not students, unless each student has exactly one.
Answer: lockers, not automatically students
A plan with two stages, or a hidden bias.
Plan A matches the 9th-grade roster.
Plan B misses students not on that app and over-represents people who like filling forms.
Answer: A is random from the grade
Every period had a chance, then students within periods had a chance. Friends are a single social cluster.
Answer: two-stage random vs cluster of friends
Adults at work or school at 2 p.m., and people without that phone line.
Answer: working adults missing
Number 1–22, draw 8 distinct random integers, survey those players. Do not pick only captains.
Answer: 8 random roster numbers
Hallways are clusters. A quiet hallway of testers is different from the cafeteria hallway. Students not in the hall at that moment have no chance.
Answer: cluster / wrong time
Wrong population. Last year is a different group, even if the method was random then.
Answer: wrong year
Get the 9th-grade roster. Number the names. Draw a random sample of 40. Ask those 40 the same question the same day.
Weakness: some drawn students are absent; replacing them carelessly can bias the sample. Self-reported minutes can also be off.
Answer: random from the roster; absences / self-report
Random means a chance process from a defined list, not a messy grab.
A grab is convenience, and the grabber’s path is a bias.
Answer: chance from a list, not a grab
The class is a cluster (same teacher, maybe same grade).
The random 25 from the school better matches the whole-school population.
Answer: random schoolwide is better
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