Question

Problem 3. Two professors teach the same course and their students have the same mean score (85) and same median score (85). Grades for each professor are listed below. Professor X: 91, 91, 82, 80, 77, 80, 93, 92, 87, 76, 86, 80, 80, 95, 85 Professor Y: 99, 83, 68, 96, 93, 75, 78, 65, 85, 96, 99, 69, 96, 98, 100, 69, 81, 99, 66 a) B. Calculate, by hand or with a software, the Mean Absolute Deviation (MAD) of each grade distribution and use this information to determine which professor’s grades have a larger variability. C. Discuss whose course would you rather be in and why.

Answer 1

MAD for Professor X = 5.33

MAD for Professor Y = 11.68

Hence, Professor Y's grades have a larger variability.

Explanation

Step 1: Data, Mean and the Absolute values for Professor X using Microsoft Excel software.

Step 2: Mean Absolute Deviation (MAD) for Professor X using Microsoft Excel software.

Step 3: Data, Mean and the Absolute values for Professor Y using Microsoft Excel software.

Step 4: Mean Absolute Deviation (MAD) for Professor Y using Microsoft Excel software.

Step 5: Variability

The higher the Mean Absolute Deviation (MAD), the greater the variability in the data; that is the data far more spread out. Hence, Professor Y's grades have a larger variability.

Step 6: Whose course would you rather be in and why?

From the results above, it is clear that Professor Y's grades are more spread out from the mean. This shows that the grades are more variable and there is quite less consistency in the grades.

However, the results show that Professor X's grades are less spread out from the mean, less variable and far more consistent.

Hence, you should rather be in Professor X's course because of the above facts.