For their final project, students in a math class are required to answer a question by collecting data about students at their school. For which of the following questions could a random sample of students provide the best approximate answer?
(A) How many students attend the school?
(B) How many hours does each class at the school meet per year?
(C) How many text messages do students at the school send per week?
(D) Do students at this school have higher test scores than students in other schools in the district?
Standards
6.SP.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
Correct answer and commentary
Student performance
At the intermediate level of the GAISE framework and in the CCSSM, students are expected to begin understanding the idea of a statistical question as one that anticipates variability in the data. Students are also expected to begin to understand various methods that could be used to sample from a population. Since the data of interest will have variability, it is necessary to use random sampling to ensure the sample is representative of the population. This question assesses student understanding of both of these concepts.
The student is required to select the question whose answer could be best approximated using a random sample of students at a school. The answer to option (A) is a deterministic one; the number of students that attend the school is a fixed number that does not vary at the time the question is being asked. It is also unclear as to how one might use random sampling to answer the question. Option (B) provides a question that could be answered using random sampling, but the population of interest is all the classes at the school. Therefore, it would make sense to take a random sample of classes at the school instead of students. The final distractor, option (D), is a valid statistical question; however, it cannot be answered using a random sample of students from only one school.