Problem 5: Making the Grade

Mr. Chips has a simple grading scheme that lends itself to
automated computation.  You will write a program that will read in
his students' grades, bonus points, and attendance record, compute
the student's grades, and output the average grade point of the
class.

Problem Statement: Mr. Chips grades as follows.  All tests are
based on 100 points and all test grades are between 0 and 100
points. If he has given more than 2 tests then he will drop the
lowest test grade for each student before computing student
averages.  After computing student averages he computes the
overall class average (mean) and standard deviation (sd). The
cutoff points for grades are: an average >= one sd above the mean is
an A, an average >= the mean but < one sd above the mean is a B,
an average >= one sd below the mean but < the mean is a C, and an
average < one sd below the mean is a D.  For every two bonus
points accrued by a student Mr. Chips increases their computed
average by 3 percentage points. Thus, if students have one bonus
point, their averages are not bumped at all.  If they have 4 or 5
bonus points, their averages are bumped by 6 percentage points,
and so on. Bumping of averages based on bonus points takes place
after the grade cutoff points have been determined.  Finally, for
every 4 absences, students lose one letter grade (from A to B, B to
C, C to D, and D to F).  For example, if they have 9 absences they
will lose two letter grades. Students cannot get a grade lower than
F. If students have perfect attendance, they gain one letter grade;
although they cannot get a grade higher than an A.  During his
computations, Mr. Chips always rounds his results to the nearest
tenth. In summary, Mr. Chips drops a student's lowest test grade if
more than 2 tests have been administered, computes each student's
average, computes the class mean and sd, adjusts the students'
averages based on bonus points, determines the student's
unadjusted grades, and then adjusts the grades based on attendance.

The average grade point of a class is determined by using 4 points
for each A, 3 points for each B, 2 points for each C, 1 point for
each D, and 0 points for each F.  The total points for the class are
added together and divided by the number of students in the class
(which is always at least 2).

The standard deviation sd of a list of numbers x1, ..., xn
is:    [graphic deleted]

If the calculated standard deviation is less than 1 then Mr. Chips
uses 1 in place of the standard deviation for grade calculation.

Suppose Mr. Chips has 5 students and has given 3 tests. The
following table shows the grades, number of bonuses and days
absent, plus the computed average (with lowest test dropped), the
adjusted average (with bonus), the unadjusted grade and the
adjusted grade (with attendance). The mean and sd used to
determine letter grade cutoffs are 69.0 and 20.1. For example, for
an unadjusted B, one's average must be greater than or equal to
69.0 and less than 89.1.

 T1   T2  T3 Bns Abst  Avg     AdjAvg   Grade  AdjGrd
100  100  80 3    2   100.0    103.0     A       A
 80   80  80 0    5    80.0     80.0     B       C
 60   20  70 5    3    65.0     71.0     B       B
 40   40  40 5    0    40.0     46.0     D       C
100   20  20 1    9    60.0     60.0     C       F         

avg grd pnt is 2.2

Input:   The first line contains an integer N between 1 and 10
describing how many of Mr. Chip's classes are represented in the
input.  The first line for each class contains two integers S and T. S
is the number of students in the class (1 < S < 31) and T is the
number of tests the students took (1 < T < 11).  The next S lines
will each represent one student in the class. A student line first lists
each of their T test scores as integers between 0 and 100 inclusive,
and then lists their bonus points and their number of absences.

Output: There should be N+2 lines of output.  The first line of
output should read MAKING THE GRADE OUTPUT.   There will
then be one line of output for each of Mr. Chip's classes showing
that class's average grade point. The final line of output should
read END OF OUTPUT.

Example:   The following input data:

3
3 2
100 50 2 5
60 60 17 1
20 10 0 0
5 5
100  80  90  80  90   0   0
80 80 80 80 80   0 0
50 50 50 50 50 0 0
100 100 20 20 20 0 0
30 30 30 30 30 0 0
10  4
79   56   59   89    4    5
100   89   96   79    6    2
80   80   80   76    1    3
76   76   76   76    5    4
58   78   67   75    4    0
100   96  100   95    1    2
47   49   46   45    0    5
67   98   59   87    5    5
23   45   52   54    2    7
78   75   79   79    3    3

should produce the following output:

MAKING THE GRADE OUTPUT
3.0
3.2
2.4
END OF OUTPUT