8A- math

Categorical (Qualitative) Variables: Describe qualities or groups where mathematical averaging is not meaningful.
- Nominal: Unordered categories with no hierarchy (e.g., blood types, native languages).
- Ordinal: Categories with a clear rank or sequence, but without measurable numerical differences between ranks (e.g., satisfaction ratings, education levels).
Numerical (Quantitative) Variables: Represent measurable amounts where standard mathematical operations are valid.
- Discrete: Arise from counting; take isolated whole values (e.g., $0$ , $1$ , $2$ items).
- Continuous: Arise from measuring; can take any real value within an interval (e.g., time, mass, $12.437\,\text{km}$ ).

Primary Data: Firsthand data gathered directly by the researcher for the specific inquiry.
- Best for: Novel questions, localized populations, and high experimental control.
- Methods: Surveys, direct measurements, observations, structured interviews.
Secondary Data: Existing data compiled and published by external organizations for another purpose.
- Best for: Large-scale national demographics, long-term trends, and cost-effective research.
- Methods: Official censuses, government databases, peer-reviewed publications.

Identify Variable Type:
- Label/Group? $\rightarrow$ Categorical (Unranked = Nominal, Ranked = Ordinal).
- Amount/Quantity? $\rightarrow$ Numerical (Counted = Discrete, Measured = Continuous).
Identify Data Source:
- Large-scale or already published by authorities? $\rightarrow$ Secondary.
- Specific, novel, or requiring firsthand control? $\rightarrow$ Primary.

Variable Classification: Classify each variable as categorical (nominal/ordinal) or numerical (discrete/continuous):
- Destination airport
- Seated passenger count
- Flight duration
- Seat class (Economy, Business, First)
Data Sources: State whether primary or secondary data is best suited for:
- Tracking an individual vehicle's real-time exhaust emissions.
- Analyzing nationwide unemployment trends over the past $10\,\text{years}$ .