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8.01 Final Renormalization of Recitation Quizzes, Fall 1998

December 21, 1998

The semifinal renormalization prescription, based on the five Recitation Quizzes and three Review Quizzes, was posted earlier. This document describes how to calculate your final renormalized Recitation Quiz average, which also takes into account the results of the Final Examination. The renormalized Recitation Quiz grades are readjusted as a result of the Final Exam only for those students for whom this adjustment results in an increase in the grade.

This document will include the formulas for computing your own renormalized Recitation Quiz grade, and also a set of grade cuts and a histogram so that you can see where you stand. The Recitation Quiz grade counts for 20% of your final grade in the course.

HOW TO COMPUTE YOUR GRADE:

STEP 1: Computation of Raw Grade

This computation is the same as it was for the semifinal renormalized Recitation Quiz average, but is repeated here for convenience. The basic idea is that each student should be allowed to drop his or her lowest quiz, and then the remaining quizzes are averaged. The implementation of this principle is complicated by the fact that in the Tues-Thurs sections one of the quizzes is to count only half, and also by the fact that some students had one or more excused absences.

Monday-Wednesday sections:

If Q1 is the lowest quiz score and Q2, Q3, Q4, and Q5 are the four others, then the desired average is:

                     Q2 + Q3 + Q4 + Q5
             <Q> =  -------------------
                             4

If the grades were not based on 100 as the maximum possible grade, then you should scale them so that they are based on 100.

Tuesday-Thursday sections:

For these sections the 3rd of the 5 quizzes should count only half as much as the others. Let Q_1/2 denote the score on the quiz that counts half, and let Q1 denote the lowest of the others. Then let Q2, Q3, and Q4 denote the remaining scores. I am assuming that the maximum possible score is 100 for all 5 quizzes. If Q_1/2 is the lowest score, then the average is

                    0.5*Q1 + Q2 + Q3 + Q4
             <Q> = -----------------------
                             3.5

If Q_1 is the lowest score, then the average is computed by

                    0.5*Q_1/2 + Q2 + Q3 + Q4
             <Q> = --------------------------
                              3.5

All students with excused absenses:

If you have any excused absences on the Recitation Quizzes, then click here to find out how to compute your raw grade.

STEP 2: Computation of Renormalized Grade

As explained with the preliminary renormalizations, we experimented with three different methods of renormalization, but found that none of them seemed to be fair in all cases. We have therefore decided to use all three, and for each student the maximum of the three calculations will be used for the renormalized grade. For each instructor, four parameters were determined by comparing the Recitation Quiz grades, the Review Quiz grades, and the Final Examination grades of the instructor's students. A table of these parameters is as follows:

TABLE OF RENORMALIZATION PARAMETERS:

		SEMI-FINAL				FINAL
Sections	Instructor	R	Q	M	B	R	Q	M	B
1	Busza	1.259	0.610	0.848	25.3	1.305	0.564	0.744	34.3
2 & 3	Burgess	0.956	1.260	1.356	-32.7	0.969	1.277	1.469	-41.6
4 & 5	Hauer	1.072	0.851	1.097	-1.8	1.044	0.911	0.985	4.5
6, 7, & 8	Javan	0.808	2.164	0.771	3.1	0.801	2.345	0.975	-15.4
9, 10, & 11	Joss	1.038	0.900	0.959	5.7	1.046	0.878	0.898	10.7
12	Koster	1.015	1.024	0.575	34.6	1.007	1.047	0.549	36.1
12 & 14	Falus	0.936	1.192	1.431	-38.6	0.938	1.154	1.419	-37.1
15, 16, & 17	Burke	0.901	1.358	1.113	-17.1	0.893	1.359	1.323	-34.6
18 & 19	Su	1.052	0.867	1.002	3.5	1.065	0.837	1.206	-9.9
20	Wiese	0.991	1.099	1.194	-16.0	0.985	1.127	0.990	-0.3
21 & 22	Millar	1.061	0.863	1.294	-16.8	1.059	0.858	1.142	-6.0
23 & 24	Graham	0.957	1.025	1.183	-16.3	0.984	0.977	1.028	-3.2
25 & 26	Katz	1.081	0.822	1.094	-0.9	1.085	0.821	1.388	-21.9

Use the parameters in the above table to compute your renormalized Recitation Quiz grades by each of the following three methods, using both the semifinal and final values of the parameters. Then take the maximum of the six calculations:

Method 1:

Renormalized Grade = R * (Raw Grade)

Method 2:

Renormalized Grade = 100 - Q*(100 - Raw Grade)

Method 3:

Renormalized Grade = M * (Raw Grade) + B

WHERE DO YOU STAND?

The passing grade for the renormalized Recitation Quiz average has been set at 62.0, and other numerical grades can be translated into letter grades according to the following chart:

A histogram of the grades is shown below:

IF YOU ARE INTERESTED:

• How were the renormalization parameters computed?

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