Math

SAT Suite of Assessments Skills Insight Tool

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Below are the skills and knowledge that students in the content domain and performance score band selected above are typically able to demonstrate as well as examples of the kinds of questions that these students are likely able to answer correctly. To view skill/knowledge statements and example questions in other domains and/or performance score bands, update the selections above and click Go.

Skills

A student in this performance score band can typically demonstrate the following skills in this content domain:

  • (SAT only) Identify or describe the population to which the results of a research study can be extended
  • Determine how the mean, median, and range of a data set are affected by changes in the data set

Example Questions

Example Question 1

Data set A consists of the heights of 75 objects and has a mean of 25 meters. Data set B consists of the heights of 50 objects and has a mean of 65 meters. Data set C consists of the heights of the 125 objects from data sets A and B. What is the mean, in meters, of data set C?

Key: 41

Key Explanation

The correct answer is 41. The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It’s given that data set A consists of the heights of 75 objects and has a mean of 25 meters. This can be represented by the equation x75=25, where x represents the sum of the heights of the objects, in meters, in data set A. Multiplying both sides of this equation by 75 yields x=7525, or x=1,875 meters. Therefore, the sum of the heights of the objects in data set A is 1,875 meters. It’s also given that data set B consists of the heights of 50 objects and has a mean of 65 meters. This can be represented by the equation y50=65, where y represents the sum of the heights of the objects, in meters, in data set B. Multiplying both sides of this equation by 50 yields y=5065, or y=3,250 meters. Therefore, the sum of the heights of the objects in data set B is 3,250 meters. Since it’s given that data set C consists of the heights of the 125 objects from data sets A and B, it follows that the mean of data set C is the sum of the heights of the objects, in meters, in data sets A and B divided by the number of objects represented in data sets A and B, or 1,875+3,250125, which is equivalent to 41 meters. Therefore, the mean, in meters, of data set C is 41.

Example Question 2

A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected 55 teams at random from all trivia teams in a certain tournament. The table displays the information for the 40 teams in the sample that practiced for at least 3 hours per week.

Hours practiced Number of points per round
6 to 13 points 14 or more points Total
3 to 5 hours 6 4 10
More than 5 hours 4 26 30
Total 10 30 40

Which of the following is the largest population to which the results of the study can be generalized?

  1. All trivia teams in the tournament that scored 14 or more points in the round

  2. The 55 trivia teams in the sample

  3. The 40 trivia teams in the sample that practiced for at least 3 hours per week

  4. All trivia teams in the tournament

Key: D

Key Explanation

Choice D is correct. It's given that the organizer selected 55 teams at random from all trivia teams in the tournament. A table is also given displaying the information for the 40 teams in the sample that practiced for at least 3 hours per week. Selecting a sample of a reasonable size at random to use for a survey allows the results from that survey to be applied to the population from which the sample was selected, but not beyond this population. Thus, only the sampling method information is necessary to determine the largest population to which the results of the study can be generalized. Since the organizer selected the sample at random from all trivia teams in the tournament, the largest population to which the results of the study can be generalized is all trivia teams in the tournament.

Distractor Explanations

Choice A is incorrect. The sample was selected at random from all trivia teams in the tournament, not just from the teams that scored an average of 14 or more points per round.

Choice B is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just the sample.

Choice C is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just a subset of the sample.