Data Analysis & Probability
Section 1: Probability in Society
Experimental vs Theoretical Probability
Experimental Probability
\[P(\text{event}) = \frac{\text{observed occurrences}}{\text{total trials}}\]
Example: 7 heads in 10 coin tosses → 7/10
Theoretical Probability
\[P(\text{event}) = \frac{\text{favorable outcomes}}{\text{possible outcomes}}\]
Example: Fair coin → 1/2 chance each side
Practice Problems
A bag has 15 red and 5 blue marbles. What's P(red)?
Theoretical probability = 15/20 = 3/4 = 75%
Section 2: Potential Data Collection Problems
Bias
"Don't you think movie prices are too high?" → Leading question
Timing
Ski jacket survey in summer vs winter
Cultural Sensitivity
Christmas-focused survey in multicultural community
Ethical Considerations
- Privacy concerns with personal data
- Proper use of collected information
- Cost vs benefit analysis
Section 3: Samples & Populations
Census
Entire population surveyed
- Costly but accurate
- Practical for small groups
Sampling Methods
- Random: Names from hat
- Systematic: Every 10th person
- Stratified: Proportional groups
Project Planning Steps
- Prepare unbiased questions
- Identify population/sample
- Collect data ethically
- Analyze & visualize results
- Evaluate methodology
Learning Resources
Key Statistics & Probability Terms and Concepts
Test your understanding of key terms and concepts!
Unit Notes (PDF)
Complete textbook chapter on probability & statistics
Khan Academy: Probability Course
Interactive videos and practice on experimental and theoretical probability
Random Sampling Tool
Use this to simulate unbiased selections and generate random numbers for data experiments