A researcher selects a sample of six professors,six students,and six administrators at a local school and has them rate the effectiveness of an innovative new teaching style.In this example,is it possible that the weighted mean ratings will equal the arithmetic mean for the entire sample of 18 participants?
A) No, the weighted mean is never exactly equal to the arithmetic mean.
B) Yes, because there are an equal number of participants in each sample.
C) Yes, because the sample sizes are selected from the same school.
D) It is not possible to know this without knowing the mean for each sample.

Question

Quizplus · Accepted Answer

Since there are equal numbers of professors, students, and administrators in the sample, their ratings will contribute equally to the overall mean, making the weighted mean equal to the arithmetic mean for the entire sample.

A Researcher Selects a Sample of Six Professors,six Students,and Six