What proportion of students who rated their instructor as very effective received a grade of C or lower?

To determine the proportion of students who rated their instructor as very effective and also received a grade of C or lower, one must analyze the dataset concerning the students' ratings and their corresponding grades. The correct answer reflects that approximately 10.2% of those students rated their instructors as very effective but nonetheless ended up receiving a grade of C or lower.

This result suggests that while a substantial portion of students may feel positively about their instructor's effectiveness, it does not always correlate with achieving higher grades. The value of 0.102 indicates that there is a noticeable segment of students (about 10 out of every 100) who, despite a high evaluation of their instructor, still face challenges in their academic performance.

Understanding this relationship is crucial in business analytics, as it highlights the importance of looking beyond surface-level assessments to identify deeper trends. It can be useful for educational institutions to analyze feedback not only for teacher evaluations but also in relation to actual student outcomes, which can inform training and support programs for instructors or interventions for students at risk of failing.

Calculating proportions like this can provide insight into the effectiveness of teaching methods and the potential disconnect between perceived and actual performance, which is vital for continuous improvement in educational practices.