Question

professor gives his class an assignment that is worth 15 points. The next day he tells his students that the mean score on the assignment was M = 11 with a standard deviation of s = 17. It should be obvious that the instructor made a mistake in his calculations. Explain why

Answer 1

Explanation:

The standard deviation (s) of the scores cannot be greater than the range of possible scores on the assignment. Since the assignment is worth 15 points, the highest possible score is 15 and the lowest possible score is 0. Therefore, the range of possible scores is 15 - 0 = 15.

If the standard deviation is 17, it means that the scores are widely spread out and there is a lot of variability in the scores, which is not possible given the limited range of possible scores on the assignment. In addition, if the mean score is 11, it means that the majority of the students did poorly on the assignment, but a standard deviation of 17 would imply that some students did exceptionally well, which is again not possible given the limited range of possible scores.

Therefore, it is clear that the instructor made a mistake in his calculations and the reported standard deviation is likely incorrect.