|
Scoreboard
and Solutions
11:00 class
|
| Grade |
W1
|
W2
|
W3
|
W4
|
W5
|
W6
|
Exam 1 |
Exam 2 |
Exam 3 |
Exam 4
|
Final |
| 90-100% |
12
|
16
|
17
|
12
|
24
|
17
|
12
|
3
|
2
|
5
|
5
|
| 80-89% |
4
|
6
|
4
|
4
|
1
|
5
|
9
|
5
|
12
|
3
|
6
|
| 70-79% |
3
|
4
|
3
|
3
|
2
|
2
|
4
|
9
|
9
|
3
|
7
|
| 60-69% |
6
|
1
|
1
|
0
|
0
|
0
|
3
|
5
|
5
|
5
|
4
|
| <60% |
3
|
0
|
1
|
1
|
0
|
1
|
3
|
8
|
1
|
9
|
6
|
| Average (%) |
78.5
|
89.5
|
90.5
|
89
|
95
|
88.5
|
80.4
|
67.6
|
76.2
|
67
|
72.0
|
1:30 class
|
| Grade |
W1
|
W2
|
W3
|
W4
|
W5
|
W6
|
Exam 1 |
Exam 2 |
Exam 3 |
Exam 4
|
Final |
| 90-100% |
4
|
10
|
7
|
6
|
14
|
3
|
8
|
0
|
3
|
4
|
3
|
| 80-89% |
5
|
3
|
5
|
3
|
0
|
0
|
5
|
5
|
4
|
3
|
3
|
| 70-79% |
6
|
1
|
2
|
3
|
0
|
1
|
4
|
4
|
3
|
2
|
6
|
| 60-69% |
2
|
2
|
2
|
1
|
0
|
1
|
2
|
3
|
5
|
4
|
3
|
| <60% |
4
|
0
|
1
|
0
|
0
|
6
|
0
|
6
|
2
|
4
|
3
|
| Average (%) |
76
|
89.5
|
83
|
84.5
|
97.5
|
65
|
84.4
|
66.8
|
74.2
|
74
|
70.7
|
| Grade |
A
| B
|
C
|
D
|
E
|
11:00 class
|
7
| 11
|
3
|
6
|
4
|
1:30 class
|
5
|
4
|
5
|
3
|
1
|
Solutions
(open in a new window, in PDF format - get Adobe Acrobat reader here)
Some are inoperative.
Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 5 Worksheet 6
Exam 1
Exam 2 Exam 3 Exam 4 Final Exam (11:00 class)
Exam 1
Exam 2 Exam 3 Exam 4 Final Exam (1:30 class)
Previous semester's exams
Exam 1
Exam 2 Exam 3 Exam 4 Final Exam
How about some inconsequential statistics?
Results of statistics and votes done in class.
Tossing a coin three times
In worksheet 5, students were asked to repeat an experiment 40 times
and record their outcomes. The experiment consisted of tossing a
coin 3 times in a row. The combined class results (1880
experiments) are in the table below. Curiously, the empirical
probability is not all that close to theoretical probability.
Tossing a coin three times (1880 experiments)
|
Combination
|
3 heads
|
2 heads, 1 tail
|
1 head, 2 tails
|
3 tails
|
Times occured
|
270
|
656
|
698
|
260
|
Empirical probability
|
.1436
|
.3489
|
.3713
|
.1383
|
Theoretical probability
|
.125
|
.375
|
.375
|
.125
|
Difference
|
.0186
|
-.0261
|
-.0037
|
.0133
|
What would you choose as a dare?
A
group of bored teenagers are deciding on what to use as a dare. The
choices are ``jump off a bridge'', ``drink kerosene'' and ``fight a
bull''. Here are your votes:
Preference rankings for each dare (1=favorite), (11:00 class)
|
| votes |
3
|
9
|
3
|
1
|
9
|
3
| Borda
points |
Jump off
bridge
|
1
|
1
|
2
|
3
|
2
|
3
| 64
(wins)
|
Drink
kerosene
|
2
|
3
|
1
|
1
|
3
|
2
| 42
|
Fight bull
|
3
|
2
|
3
|
2
|
1
|
1
| 62
|
Preference rankings for each dare (1=favorite), (1:30 class)
|
| votes |
4
|
6
|
1
|
0
|
5
|
0
| Borda
points |
Jump off
bridge
|
1
|
1
|
2
|
3
|
2
|
3
| 42
(wins)
|
Drink
kerosene
|
2
|
3
|
1
|
1
|
3
|
2
| 22
|
Fight bull
|
3
|
2
|
3
|
2
|
1
|
1
| 32
|
What you would drink with dinner?
Plurality election, 29 votes (11:00 class)
|
| Soda |
16
|
| Juice |
3
|
| Water |
10
|
| Plurality election, 17 votes (1:30 class)
|
| Soda |
9
|
| Juice |
3
|
| Water |
5
|
Given a couple of hours of free time, what pastime would you choose?
Preference rankings for each pastime (1=favorite), (11:00 class)
|
| votes |
6
|
9
|
5
|
2
|
6
|
2
|
| Movie |
1
|
1
|
2
|
3
|
2
|
3
|
| Video-game |
2
|
3
|
1
|
1
|
3
|
2
|
| Internet |
3
|
2
|
3
|
2
|
1
|
1
|
From the table we get the following results, using various voting methods:
Plurality election:
Movie: 15
Video-game: 7
Internet: 8
|
Runoff:
Movie: 20 (wins)
Internet: 10 |
Borda's method:
Movie: 71 (wins)
Video-game: 52
Internet: 57
|
Head-to-head comparison:
Movie : Video-game, 21:9
Movie : Internet, 20:10
Video-game : Internet, 13:17
Movie is the Condercet winner
|
Preference rankings for each pastime (1=favorite), (1:30 class)
|
| votes |
6
|
7
|
0
|
0
|
3
|
0
|
| Movie |
1
|
1
|
2
|
3
|
2
|
3
|
| Video-game |
2
|
3
|
1
|
1
|
3
|
2
|
| Internet |
3
|
2
|
3
|
2
|
1
|
1
|
From the tables we get the following results, using various voting methods:
Plurality election:
Movie: 13
Video-game: 0
Internet: 3
|
Runoff:
Movie: 13
Internet: 3 |
Borda's method:
Movie: 45 (wins)
Video-game: 22
Internet: 29
|
Head-to-head comparison:
Movie : Video-game, 16:0
Movie : Internet, 13:3
Video-game : Internet, 6:10
Movie is the Condercet winner
|
If the whole class had dinner paid for, what meal would we eat?
Approval method, 29 votes (11:00 class)
|
| votes |
4
|
1
|
4
|
4
|
6
|
6
|
1
|
3
| Totals
|
Roast pork Parisienne
|
|
|
x
|
|
|
x
|
x
|
x
| 14
|
Peking Duck
|
|
|
|
x
|
|
x
|
x
|
| 11
|
Burger w/fixin's
|
x
|
|
x
|
x
|
x
|
x
|
|
x
| 27 (wins)
|
Vegetarian plate
|
|
x
|
|
|
x
|
|
x
|
x
| 11
|
Approval method, 29 votes (1:30 class)
|
| votes |
2
|
1
|
2
|
4
|
4
|
1
|
2
| Totals
|
Roast pork Parisienne
|
|
|
x
|
|
x
|
x
|
x
| 9
|
Peking Duck
|
|
|
|
x
|
x
|
|
x
| 7
|
Burger w/fixin's
|
x
|
|
x
|
|
x
|
x
|
x
| 11 (wins)
|
Vegetarian plate
|
|
x
|
|
x
|
|
x
|
x
| 2
|
|
|