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Problem-Solving and Data AnalysisMediumChoosing a representative sample

Problem-Solving and Data Analysis practice question

A principal wants to estimate the percent of the 1,200 students at her school who cycle to school. Which of the following sampling methods is most likely to give a representative sample?

  1. A. Choosing 100 students at random from the school's full enrolment list and asking each one.Correct
  2. B. Asking the first 100 students who arrive at the bicycle racks one morning.
  3. C. Asking every member of the school's cycling club.
  4. D. Posting a survey on the school website and using the responses of whoever chooses to reply.

Answer: A. Choosing 100 students at random from the school's full enrolment list and asking each one.

Random selection from the whole population gives every student the same chance of being chosen, so the sample resembles the school as a whole.

Why the other answers are wrong

B. Asking the first 100 students who arrive at the bicycle racks one morning.
Students at the bicycle racks are, by definition, cyclists. That sample would put the estimate near 100%.
C. Asking every member of the school's cycling club.
The cycling club is the group MOST likely to cycle; it can't stand in for all students.
D. Posting a survey on the school website and using the responses of whoever chooses to reply.
People who choose to reply differ from those who don't — for instance, students with strong feelings about cycling. That is a self-selected sample.

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