One common kind of inductive argument reasons from a sample to a whole group: "Most students I surveyed want a longer lunch, so most students at school do." How strong it is depends on the sample.
Key idea
A generalization is only as good as its sample. A good sample is large enough and representative: chosen fairly, so it is like the whole group in the ways that matter to the question.
Why it works
A sample stands in for a group we cannot check one by one. If it is tiny, chance can make it look very different from the group. If it is chosen in a slanted way, it will differ from the group in a steady direction, and making it bigger only repeats the slant.
Worked example: Big but biased
To learn the favorite sport of students at a middle school, Jamal surveyed 300 people at a basketball game. Is this a good sample?
- 300 is a decent size.
- But people at a basketball game are more likely than other students to love basketball.
- The sample is not like the whole school on this question.
Answer: No: it is biased, however large.
Worked example: Small but random
Rosa asked 4 friends whether students want more clubs. Is this a good sample of the school?
- Four people is far too few: a different four could give different answers.
- Friends also tend to share interests.
Answer: No: too small (and probably not typical).
Common mistake
Trusting a huge sample that was chosen in a biased way, like asking only chess club members which game students like best. Size does not cure bias. Ask how the people were chosen before asking how many there were.