Statistics Unit 1: Introduction

Questions and Answers

What is the plural sense of statistics?

Set of numerical figures

What is the singular sense of statistics?

The branch of science that deals with the collection, presentation, organization, analysis, and interpretation of data

What term is used for a subset of the population?

Sample

What is a variable?

A characteristic or attribute of the elements in a collection that can assume different values Signup and view all the answers

What does a parameter describe?

Specific characteristic of the population Signup and view all the answers

What is the difference between a parameter and a statistic?

A parameter describes a population; a statistic describes a sample Signup and view all the answers

What does the population refer to in statistics?

The collection of all elements under consideration Signup and view all the answers

The proportion is the quotient obtained when the magnitude of the part is divided by the magnitude of the ______.

whole Signup and view all the answers

Which of the following represents the singular sense of statistics?

Branch of science dealing with data analysis Signup and view all the answers

What is an observation?

Realized value of a variable Signup and view all the answers

What is the notation for population size?

N Signup and view all the answers

What is the notation for sample size?

n Signup and view all the answers

Study Notes

Learning Outcomes

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

Basic Concepts

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.

Key Terms

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.

Examples of Variables and Observations

S: sex of a student (Male, Female)
E: employment status of an employee (Temporary, Permanent, Contractual)
I: monthly income of a person (≥ 0 pesos)
N: number of children of a teacher (0, 1, 2, 3, …)
H: height of a basketball player (> 0 cm)

Population and Sample Example

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.

Parameters and Statistics

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).

Proportional Example

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.

Estimation

Aim to estimate the true proportion of a specific characteristic (e.g., cellphone ownership) within a population based on sample data.

Description

This quiz covers the fundamental concepts of statistics as introduced in Unit 1. You will learn to define key terms, differentiate between theoretical and applied statistics, and understand the steps in statistical inquiry. Test your knowledge and enhance your understanding of this essential field.