2. Populations and Samples Text(1)

Population: A population is a complete set of individuals or objects of interest.
- Example populations:
  - Every citizen of the United States.
  - Every coffee sold last year.
  - Every good manufactured by a certain company in a given year.
  - Every member of a species of African elephants.
Population Size: Denoted by 𝑁, refers to the number of individuals in a population, which can potentially be infinite.
Variables: Attributes or characteristics of individuals in the population used to describe them.
- Example variables:
  - State of residence for citizens.
  - Size of coffee sold.
  - Number of defects on a manufactured good.
  - Weight of an African elephant.
A well-defined variable assigns a single value to each individual. Values examples:
- California (for state variable).
- Large (for size variable).
- 18 defects (for defects variable).
- 4,000 kg (for weight variable).
Variables are crucial for specifying populations. They help define populations through attributes like sex, age, and state.

Qualitative Variables: Assign categories to individuals.
- Nominal Variables: No natural order.
  - Example: state of residence.
- Ordinal Variables: Have a natural order.
  - Example: size of coffee sold (Small, Medium, Large).
Quantitative Variables: Assign numerical values to individuals, always with a natural order.
- Requires a unit of measurement (e.g., inches, years).
- Discrete Variables: Countable values (e.g., number of defects).
- Continuous Variables: Measurable quantities (e.g., weight of an elephant).

The population distribution describes the values of a variable in a population. The sample is a manageable subset of the population used for analysis when the entire population isn't accessible.
Each value in a sample is known as a datum or observation.
The distribution of the values in a sample is termed sample distribution.
Dataset example with citizens of the U.S. represented in a table with variables.
The number of individuals in a sample is called sample size, represented by 𝑛.

Descriptive Statistics: Deals with collecting, visualizing, and summarizing data from a sample.
Inferential Statistics: Involves making conclusions about populations based on sample data collected.

Good Data Collection: Begins with clearly stating the statistical question regarding the distribution of variables in populations.
A statistical question involves defining the population and the variables of interest.
Sampling Design: Methodology used to obtain a representative sample from a population to mitigate bias.
Examples of biased sampling:
- Convenience Sample: Sampling individuals easiest to reach (e.g., classmates for SAT scores).
- Voluntary Response Sample: Participants self-select (e.g., voting on a television show).

Response Bias: Influences how participants respond (e.g., social desirability bias).
Ensure fairness through anonymity and neutral wording in surveys.
Simple Random Sample (SRS): Every combination of individuals has the same probability of being selected, using random digit tables for selection.

Survivorship Bias: Noting the harm done to surviving samples can skew results, e.g., WWII aircraft armor decisions.
Example of well-known bias impacts on research findings and decision-making.