SAT Math Multiple Choice Question 186: Answer and Explanation

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Question: 186

6. The student council at Shermer High School wants to use student opinion to decide on one of three possible homecoming themes for the year. President Peterson thinks that the best way to determine popular opinion is for each of the 10 members of the student council to poll 10 of their friends and select the theme that receives the most votes. Vice President Vaidya wants to go to the cafeteria during lunch and poll 100 students to determine the winner. Treasurer Thompson says the best method would be to assign numbers to each of the 1,000 students in the school, randomly select 100 of them to poll, and select the winner based on the results. Secretary Stephens argues that they must poll each of the 250 members of the senior class to find the most popular theme. Whose method is most likely to accurately determine overall student opinion regarding the most popular homecoming theme?

  • A. President Peterson
  • B. Secretary Stephens
  • C. Treasurer Thompson
  • D. Vice-President Vaidya

Correct Answer: C

Explanation:

C Two factors are important in determining how to poll a group: the size of the sample and how that sample is selected. Secretary Stephens's plan has the largest sample with 250 students, but all those students belong to the senior class. Perhaps the senior class would prefer a theme that the other three classes would not. The sample is skewed and not necessarily representative of the entire student body, so eliminate (B). The other three plans all poll 100 students, so the manner in which those students are selected becomes more important. President Peterson's plan is also skewed specifically to friends of the student council members, whose opinions might not reflect the majority, so eliminate (A). Vice President Vaiyda's plan has more potential for a varied sample, but it is still not as good as Treasurer Thompson's plan, which guarantees that a random assortment of people will be chosen for the poll. Eliminate (D), and choose (C).

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