1. Voting Systems
Plurality Method
Step 1: Look at first choice votes only.
Step 2: Find the biggest number.
That person wins.
Practice question:
First choice votes: D=26, E=27, F=28, H=29
H has 29. Answer: Hawking (H)
Borda Count
For 3 candidates:
1st place = 3 points
2nd place = 2 points
3rd place = 1 point
Add the points for each person. Highest total wins.
Plurality with Elimination
Step 1: Find person with fewest votes.
Step 2: Remove that person.
Step 3: Repeat with remaining people until one has more than half the votes.
2. Statistics
Mean
Add all numbers. Divide by how many numbers there are.
Frequency table example (from your notes):
Scores: 1, 2, 3, 4, 5, 6, 7, 8
Frequency: 2+, 4,+ 3, +4,+ 5, +4,+ 2, +3
Do: (1×2) + (2×4) + (3×3) + (4×4) + (5×5) + (6×4) + (7×2) + (8×3) = 122
Total frequency = 27
Mean = 122 ÷ 27 = 4.52
Median
Put numbers in order from smallest to biggest.
If odd number of values: middle one.
If even: add the two middle numbers and divide by 2.
Mode
The number that appears the most times.
Midrange
(lowest number + highest number) ÷ 2
3. Probability & Combinatorics
Combination (order does not matter)
Use formula: n! / (k! × (n-k)!)
Example from your notes: 45! / (7! × 38!) = 45,379,620
Probability
Favorable outcomes ÷ total possible outcomes.
Example: 4 good outcomes out of 36 = 4/36 = 1/9
