2020 has been an interesting year, to say the least. COVID-19, earthquakes, murder hornets, and a rejuvenated civil rights movement have all hit the headlines in the first half of the year. As we enter the summer, however, the drama dial will be turned up to 11 as the next wave of chaos rolls in: the 2020 presidential election. And as part of that process, Americans will be inundated with surveys and polls. Even standardized test takers aren’t immune! Understanding surveys and polls on the SAT is an integral part of success on the math sections.
We’ll take a look at a couple of examples of polling and survey questions on the test and talk you through the strategy behind them.
Question 1: How to create a successful poll
A political scientist wants to predict how the residents of New Jersey will react to a new bill proposed in the state senate. Which of the following study designs is most likely to provide reliable results for the political scientist?
A) Mailing a questionnaire to each of 300 randomly selected residents of New Jersey
B) Surveying a group of 200 randomly selected New Jersey residents
C) Interviewing a group of students randomly selected from a large public university in New Jersey
D) Surveying a group of 1,500 randomly selected US residents
Any ideas? This is a fairly straightforward question that tests students on what makes a survey valid. Students can usually eliminate choices C) and D) because they don’t involve New Jersey residents directly.
But A) and B) can be a little more tricky. A) seems like the right choice at first glance because the survey involves more respondents–if it weren’t for the fact that the success of a questionnaire is dependent on a person returning it. Would all 300 residents return the survey? And, as I often ask my students, who returns a mailed questionnaire? A person who has a more pressing or direct interest in the issue! So while the political scientist may get some data from the questionnaire, a far more reliable method would be to directly survey a random group of state residents.
Question 2: What do the poll results mean?
A city with 120,000 residents is voting on a proposal that would eliminate overnight parking of vehicles on the city’s streets. An independent company randomly surveys 1,200 residents to see whether or not residents would support this proposal. The outcome of the survey shows that 60% of the residents surveyed approve of the proposal with a margin of error of 2%. Which of the following statements is a plausible conclusion from the outcome of the study?
A) Exactly 60% of city residents approve eliminating overnight parking.
B) There are 72,000 city residents who approve eliminating overnight parking.
C) About 2% of the city residents do not approve eliminating overnight parking.
D) Between 58% and 62% of the city residents approve eliminating overnight parking.
In this question, the survey has already been completed and the results are in: 60% of people approved eliminating overnight parking with a margin of error of 2%. This question is focused on just what that result means.
We can eliminate choice A) because of one word: exactly. While a well-done poll can give a predicted result that is very close to reality, it’s still just that–a prediction. Even under the best of conditions, it’s not an exact science. One only needs to look at predictions surrounding recent elections to see how unscientific polls can be.
B) is an attractive choice because it looks like it might require some math. Surely the SAT would want us to calculate something in a math question! And, in fact, 60% of 120,000 is 72,000. The problem, however, comes back to the exactness of that result. A poll is always a prediction. So to say that 72,000 people would approve is far too precise for any poll. If the answer had said, “Around 72,000 city residents will likely approve…”, it would be far closer to the truth.
That leaves us with C) or D), and the choice between the two comes down to an understanding of the term “margin of error.” Because polls are only predictors, polls are often presented with a bit of wiggle room. Our poll said that 60% of people approved eliminating overnight parking. That 2% margin of error is just that: a range in which the truth might actually lie. And choice D) reflects that idea. According to the poll results, the correct percentage that approves could be anywhere between 58% and 62%, given the margin of error.
The most important strategy to use with questions about surveys and polls on the SAT is an important strategy for every question on the test: read carefully. The test writers aren’t doing you any favors, and they’ll word things in convoluted ways just to make it tougher on you. If you’re working too quickly, it can be easy to overlook words like “exactly” or “likely,” and those types of words can be incredibly important. So take a breath and read that question carefully.
Practicing on actual SATs is also helpful. Poll and survey questions appear in the no-calculator and/or calculator sections of nearly every SAT, and the more of them you see and work through, the less likely that you’ll be duped by a trick. So putting in the time to practice is essential to be successful on these questions, as well as all the other types you’ll see on a typical SAT.