Overview
This lecture introduces the key statistical symbols and helps distinguish between sample statistics and population parameters using practical examples.
Parameters vs. Statistics
- Parameters describe a whole population (e.g., μ, σ, P, π, N, β₀, β₁).
- Statistics describe a sample from the population (e.g., x̄, s, p̂, n, b₀, b₁).
- Recognizing these symbols is essential for entering correct values in statistical software.
Example 1: IQ Test Data
- Population mean (μ) = 100 (parameter).
- Population standard deviation (σ) = 15 (parameter).
- Sample size (n) = 45 (statistic).
- Sample mean (x̄) = 97.7 (statistic).
- Sample standard deviation (s) = 15.3 (statistic).
Example 2: Voting Poll
- Sample size (n) = 200 (statistic).
- Sample proportion (p̂) = 0.472 (statistic; convert percent to decimal for software).
- Population proportion (π or P) = 0.413 (parameter; represents the actual population result).
Practice and Application
- It is important to identify whether numbers are statistics (from samples) or parameters (from populations).
- Be comfortable matching symbols to values when inputting data into statistical programs.
Key Terms & Definitions
- Parameter — a value describing a population (e.g., μ, σ, P, π).
- Statistic — a value describing a sample (e.g., x̄, s, p̂).
- μ (mu) — population mean.
- σ (sigma) — population standard deviation.
- N — population size.
- x̄ (x-bar) — sample mean.
- s — sample standard deviation.
- n — sample size.
- P — population proportion.
- π (pi) — population proportion (alternative notation).
- p̂ (p-hat) — sample proportion.
Action Items / Next Steps
- Practice identifying and matching statistical symbols to values in similar problems.
- Review and memorize key symbols for use in upcoming classwork and software.