Introduce the concept of statistics, its importance in various fields, and the types of data that are analyzed using statistical methods.
| Branch | Primary Focus | Typical Applications |
|---|---|---|
| Descriptive Statistics | Summarizes and visualizes data | Reporting sales totals, summarizing survey results |
| Inferential Statistics | Draws conclusions about a larger population from a sample | Clinical trials, opinion polling, quality control |
| Data Type | Scale | Examples |
|---|---|---|
| Nominal | Categorical, no order | Gender, blood type |
| Ordinal | Categorical, ordered | Survey rating (poor‑good‑excellent) |
| Interval | Numeric, equal intervals, no true zero | Temperature in °C |
| Ratio | Numeric, equal intervals, true zero | Height, weight, income |
| Concept | Description |
|---|---|
| Experiment | Procedure producing outcomes. |
| Sample Space (Ω) | Set of all possible outcomes. |
| Event | Subset of Ω. |
| Probability (P) | Numerical measure 0 ≤ P(event) ≤ 1 satisfying Kolmogorov axioms. |
| Conditional Probability | (P(A |
| Independence | (P(A\cap B)=P(A)P(B)). |
| Method | Key Idea | When to Use |
|---|---|---|
| Simple Random Sample | Every unit has equal chance. | Small, homogeneous populations. |
| Stratified Sampling | Divide into strata, sample proportionally. | Heterogeneous groups where sub‑populations matter. |
| Cluster Sampling |