Posted by: jeff | October 21, 2010

## Midterm Results

Here are the statistics from the midterm exam:

• Average: 51
• Median: 55
• Standard Deviation: 21

Although we’d like to have seen the average somewhere in the 60-70 range, the overall performance was good.  The grades ranged up to the 80s, but the Std. Deviation is much lower than on most of the homeworks so far, so the grades are more tightly grouped around the average.

Here is the rubric we used to evaluate your exams (the person who graded each question is in parentheses):

1. (Alex) For each of the T/F questions:
• If the judgment is wrong, all 10 points are deducted.
• If the judgment is right:
• if the justification is totally wrong or meaningless, 6 points are deducted
• if the justification has something(although it is not able to support the judgment), 5 points are deducted
• if the justification are partially correct(by mentioning something that’s relevant to the correct idea only), 3 points are deducted
• if the justification is right(by presenting the correct idea or example), full points are given
2. (Part a – Atri, Parts b & c – Jeff)
• a) Most of you got this right. In general the rubric I followed was the following. +2 for pretty much writing anything. +2 extra if there was some substance to answer but it was clear that you did not quite understand the problem. -6 points if there was no argument for the stability of the perfect matching (but everything else was correct).
• b) For a valid argument for n=3, +5 points.  For a partially valid argument, or a single example for n=3, +2-3 points. Or, for the general odd case: full credit (+25) for a valid argument using the definitions; most of the credit (+20) for a mostly valid argument (often the right ideas, but imprecise from not using the definitions); partial credit (+5-15) for an argument which contains some valid point or idea, but without fully justifying the claim. No credit for an irrelevant, meaningless, or incorrect answer for either the n=3 or general odd case.
• c) Proving that the algorithm does not always output a stable matching for even n means showing that there exists at least one case where it doesn’t.  Either providing a specific counterexample (an instance of the HSMP where it doesn’t work) or arguing a general case for the circumstances where the algorithm would fail earned you full credit (+10).  Mostly correct arguments and slightly incomplete counterexamples (i.e. order of choosing free entities not specified, preference lists are partially wrong or not fully specified) received most of the credit (+7-8).  Arguments and counterexamples with only some valid ideas received some partial credit (+2-5).  Irrelevant, meaningless, or fully incorrect answers received no credit.
3. (Atri) +2 points if correctly state that the diameter is $2d$. +4 more if state that the apd is around $d$. The rest of the 4 points for formally arguing that the ratio is $O(1)$. 1 point if none of the above done but computed the ratio for one (somewhat non-trivial) instance.

Please be sure you review the feedback written on your graded exam as well as this rubric, and give the questions some further thought, before you come to discuss questions about grading with us.