There are two 6th grade classes at a middle school. Each class has 15 boys and 15 girls. In one class the mean height of students is 64 inches. From the information provided, what must be true about the mean height for the students in the other class?
(A) The mean height for the students in the other class is 64 inches.
(B) The mean height for the students in the other class is less than 64 inches.
(C) The mean height for the students in the other class is more than 64 inches.
(D) The mean height for the students in the other class cannot be determined.
Standards
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.
S-IC.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Correct answer and commentary
Student performance
The correct answer for this question is Option (D). Statistics is a problem-solving process focused on the study of variability. One focus of statistics is on the claims that can be made as a result of conducting certain types of studies. An equally important topic is what claims cannot be made. Just because data from one class have been collected does not mean we can make specific claims about a different class that shares some similar characteristics, based on those data. Of course, it may be reasonable to suspect that if the mean for one class is 64 inches that the mean for a similar class may be near 64 inches, but we cannot make specific claims such as that one with certainty.
While the context of this question is straightforward, the underlying problem is critically important to the work of practicing statisticians. The claims that are made from interpreting the results of statistical analyses must be appropriate to the conditions and assumptions surrounding the data collection.