Which Professor? Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You need to decide which professor to take the class from and have just completed your Introductory Statistics course. Records obtained from past students indicate that students in Professor Alpha’s class have a mean score of 80% with a standard deviation of 5%, while past students in Professor Omega’s class have a mean score of 80% with a standard deviation of 10%. Decide which instructor to take for Introductory Biology using a statistical argument.

Verified step by step guidance

1. Identify the key statistics for each professor's class: both have the same mean score of 80%, but Professor Alpha's class has a standard deviation of 5%, while Professor Omega's class has a standard deviation of 10%.
2. Understand that the mean score represents the average performance, while the standard deviation measures the variability or consistency of scores around the mean.
3. Since both professors have the same average score, focus on the standard deviation to assess which class might be more predictable or consistent in terms of student performance.
4. Recognize that a smaller standard deviation (Professor Alpha's 5%) indicates that students' scores tend to be closer to the mean, suggesting more consistent outcomes, whereas a larger standard deviation (Professor Omega's 10%) implies more variability in scores.
5. Based on this statistical reasoning, decide which professor to choose by considering whether you prefer a more consistent performance (lower variability) or are comfortable with greater variability in potential outcomes.

Key Concepts

Mean and Standard Deviation

The mean represents the average score of students in each professor's class, indicating central tendency. The standard deviation measures the variability or spread of scores around the mean, showing how consistent the students' performances are. Both metrics help compare the overall performance and reliability of each professor's class outcomes.

Variability and Consistency

Variability refers to how spread out the students' scores are within a class. A lower standard deviation means scores are more tightly clustered around the mean, indicating consistent performance. Higher variability suggests less predictability in outcomes, which can influence the decision if consistency is valued.

Statistical Decision-Making

Statistical decision-making involves using data summaries like mean and standard deviation to make informed choices. Here, comparing the two professors' score distributions helps assess which class might offer a more predictable or stable learning outcome. This approach applies statistical reasoning to practical decisions.