Statistics Unit 1: Introduction

Study Notes

Understand basic statistical terms.
Differentiate between mathematical/theoretical statistics and applied statistics.
Enumerate steps involved in statistical inquiry.

Definition of Statistics:
- Plural: Refers to numerical figures (e.g., athlete statistics).
- Singular: Science focusing on data collection, presentation, organization, analysis, and interpretation (COPAI).
Importance of Statistics:
- Transforms large data volumes into meaningful information for better decision-making.
- Facilitates intelligent choices through empowered information use.

Population: Denoted by N; encompasses all elements in a statistical inquiry.
Sample: Denoted by n; a subset of the population for analysis.
- Elements may include individuals, objects, animals, or regions (e.g., farmers in Negros Occidental).
Variable: A characteristic that can take different values (e.g., age, weight, height).
Experimental Unit: The individual/object on which a variable is measured (e.g., age of a student, weight of mangoes).
Observation: The realized value for a given variable.
Data: Collection of observations.

Study Example: Relationship between entrance exam scores and general weighted average (GWA) of university graduates (2000-2005).
- Population: All graduates from 2000-2005.
- Sample: Graduates from a specific department within that range.
- Variables: Entrance exam scores and GWA.
- Observations: Individual scores and GWAs.

Parameter: Summary measure of a population characteristic, often denoted by Greek letters (e.g., μ for mean).
Statistic: Summary measure describing a sample characteristic (e.g., sample mean).
Proportion: Represents the part-to-whole relationship, calculated as:
- P = (Number of elements with a certain characteristic) / (Total elements in collection).

Population Example: 20 students in a Statistics course concerning cellphone ownership.
- Variable: Cellphone ownership (0 for no, 1 for yes).
- Population Proportion: If 15 students own a cellphone,
  - P = 15 / 20 = 0.75.
Sample Example: In a sample of 10 students, if 7 own cellphones,
- P̂ = 7 / 10 = 0.7.
- Distinction: P is a parameter; P̂ is a statistic.