Overview
This lecture explains the foundational statistical concepts of populations and samples, their differences, related symbols, and how samples inform us about populations.
Populations
- A population consists of every individual or item belonging to a defined group.
- Examples: all citizens of a country, every pair of pants made by a company.
- Population values are called parameters.
Population Symbols (Parameters)
- Mu (μ): Population mean (average).
- P: Population proportion.
- Sigma (σ): Population standard deviation.
- Capital N: Population size.
- Rho (ρ): Population correlation coefficient.
Samples
- A sample is a smaller subset taken from a population.
- Examples: 1,000 citizens from a region, every fourth pair of pants.
- Sampling methods can vary but the key point is that a sample represents part of the population.
- Sample values are called statistics.
Sample Symbols (Statistics)
- X-bar ((\bar{x})): Sample mean.
- P-hat ((\hat{p})): Sample proportion.
- S: Sample standard deviation.
- Lowercase n: Sample size.
- R: Sample correlation coefficient.
Using Samples to Understand Populations
- We often want to learn about a population, but measuring everyone is unrealistic.
- By analyzing a sample, we can estimate characteristics of the broader population using statistical methods.
Key Terms & Definitions
- Population — Entire set of individuals or items of interest.
- Sample — Subset of a population selected for study.
- Parameter — Numeric summary describing a population.
- Statistic — Numeric summary describing a sample.
Action Items / Next Steps
- Review and memorize the population and sample symbols.
- Prepare for upcoming lessons on using samples to infer population properties.