AP Statistics 4.1 Introducing Statistics: Random and Non-Random Patterns?Study Notes
AP Statistics 4.1 Introducing Statistics: Random and Non-Random Patterns? Study Notes- New syllabus
AP Statistics 4.1 Introducing Statistics: Random and Non-Random Patterns? Study Notes -As per latest AP Statistics Syllabus.
LEARNING OBJECTIVE
- Given that variation may be random or not, conclusions are uncertain.
Key Concepts:
- Introducing Statistics: Random and Non-Random Patterns
Introducing Statistics: Random and Non-Random Patterns
Introducing Statistics: Random and Non-Random Patterns
Statistics begins with identifying whether data reflect random variation or a meaningful pattern. Randomness is central in probability and sampling, while non-randomness may indicate bias or a real underlying relationship.
Random Patterns
- Arise naturally from chance processes such as coin flips, dice rolls, or random sampling.
- Show short-term irregularity but predictable long-term behavior (Law of Large Numbers).
- Do not follow a fixed, repeating sequence, even if clusters or streaks appear.
- Provide fairness in experiments by balancing out lurking variables.
- Example: Flipping a fair coin 10 times may give “HHH” streaks, but the process is still random.
Non-Random Patterns
- Suggest influence beyond chance, such as bias, confounding, or a real relationship.
- Often appear systematic, repeating, or predictable.
- May result from flawed data collection methods (e.g., undercoverage, voluntary response bias).
- Can be useful if they reflect genuine cause-and-effect relationships in experiments.
- Example: A survey taken only online may consistently underestimate older populations.
Comparison Table
| Feature | Random Pattern | Non-Random Pattern |
|---|---|---|
| Cause | Chance process (coin flip, dice roll, random selection) | Systematic influence (bias, design flaw, real effect) |
| Appearance | Irregular, clusters or streaks possible, no repeating cycle | Predictable, repeating, or consistently skewed |
| Interpretation | Expected variation; does not imply bias or effect | May indicate a real association, bias, or error |
| Example | 10 coin flips yield “HHHTHTTTTH” | Survey always underestimates older populations |
Example
You flip a fair coin 6 times and get “HHHHHH.” Does this mean the coin is biased?
▶️ Answer / Explanation
Step 1: Even though the sequence looks unusual, each outcome has probability (1/64).
Step 2: Random processes can produce streaks.
Conclusion: This result alone is not evidence of bias. It can happen by chance.
Example
A store surveys customers only in the morning and concludes that most shoppers are retirees. Is this pattern random?
▶️ Answer / Explanation
Step 1: Data collection excluded evening shoppers (working adults).
Step 2: This is a systematic bias, not chance.
Conclusion: The pattern is non-random, caused by flawed sampling design.
Example
In a clinical trial, patients randomly assigned to a new drug group show much lower blood pressure than the placebo group, with p-value < 0.01. Is this random variation?
▶️ Answer / Explanation
Step 1: Random assignment balances groups on average.
Step 2: A p-value < 0.01 means chance alone is very unlikely to explain results.
Conclusion: This is a non-random effect caused by the treatment, not chance.