Statistics and Probability: Lesson 1

Course Information

• Course title: Statistics and Probability
• Course code: MATH03
• Lesson 1: Introduction to Statistics and Probability
• University: Mapúa University

Objectives

• Students will be able to apply statistical concepts to real-world problems.
• Students will be able to calculate appropriate sample sizes.
• Students will be able to differentiate between parameters and samples.
• Students will be able to classify different types of variables.
• Students will be able to illustrate random variables (discrete and continuous).
• Students will be able to distinguish between discrete and continuous random variables.

Definition of Statistics

• Statistics is the science of collecting, analyzing, presenting, and interpreting data.
• It also involves making decisions based on this analysis.

Two Aspects of Statistics

• Theoretical/Mathematical Statistics: Focuses on developing, deriving, and proving statistical theorems, formulas, rules, and laws.
• Applied Statistics: Focuses on applying theoretical statistical concepts to solve real-world problems.

Two Aspects of Applied Statistics

• Descriptive Statistics: Organizing, displaying, and describing data using tables, graphs, and summary measures.
• Inferential Statistics: Using sample results to make decisions or predictions about populations.

Examples of Descriptive Statistics

• A supervisor wants to know the average salary of 40 clerks.
• A market researcher creates a graph showing sales fluctuations over three years.
• A school survey reveals student opinions on a proposed charter change.

Examples of Inferential Statistics

• A tire dealer estimates the average lifespan of a particular tire brand.
• A company predicts a 50% increase in revenue over five years based on past data.

Population and Sample

• Population: The complete set of individuals, objects, places, items, events, or measurements of interest.
• Target Population: The specific population being studied.
• Sample: A portion or part of the population selected to represent the population.
• Populations can be:
  • Finite: A population with a limited number of members.
  • Infinite: A population with an unlimited number of members.

Examples of Finite Populations

• Children attending school in Butuan City.
• Prices of mathematics books published in the Philippines over three years.
• Cards in a deck.
• Percentage of all females earning less than Php100,000 per year.

Examples of Infinite Populations

• Possible rolls of a die.
• Possible observations in a specific experiment.

Survey and Sample Surveys

• Survey: The collection of information from elements of a population or a sample.
• Sample Survey: A technique collecting information from a portion of the population.
• Census: A survey that includes every element of the target population.

Why Take Samples Instead of the Entire Population?

• It's often impractical or infeasible to study every member of a large population.

Determining the Sample Size (Slovin's Formula)

• Formula: n = N / (1 + Ne²)
• Where:
  • n = Required sample size
  • N = Size of the finite population.
  • e = Margin of error (typically 1% to 10% in social science research).

Examples of Variables

• Quantitative Variable: A variable that is classified according to numerical value.
  • Discrete Variable: A variable that can assume only specific values. -Examples: number of days, number of children in a family, number of students, etc
  • Continuous Variable: A variable that can take on any value within a certain range. -Examples: weight, height, volume, etc
• Qualitative Variable: A variable that can be classified into categories based on characteristics or attributes.
  • Dichotomous Variable: A variable that can be classified into only two categories (e.g., yes/no).
  • Multinomial Variable: A variable that can be classified into more than two categories (e.g., highest educational attainment).

Levels of Measurement

• Nominal: Classifies data into categories without any inherent order.
  • Examples: Gender, Political Affiliation, Nationality.
• Ordinal: Classifies data into categories with an inherent order.
  • Examples: Honor Roll, Ranking of Faculty Members.
• Interval: Shows the order of cases and the exact differences between cases, but it does not have a true zero point. -Examples: Temperature, Examinations (scores), Longitude and Latitude.
• Ratio: Possesses all characteristics of an interval scale and has a true zero point. -Examples: Measurements of weight, height, length, age.

This quiz covers the foundational concepts of statistics and probability as introduced in Lesson 1 of the course. Students will explore key definitions, differentiate between various types of variables, and develop an understanding of both theoretical and applied statistics. Perfect for those looking to strengthen their grasp on the basics of statistical analysis.