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STAT/MATH 3379: Elementary Statistics - Chapter 1 Notes

STAT/MATH 3379: Elementary Statistics / Statistical Methods in Practice

Chapter 1: Getting Started

This chapter introduces fundamental concepts in statistics, laying the groundwork for understanding how data is collected, organized, analyzed, and interpreted.

1.1 What is Statistics?

  • Data

    • Consists of information derived from observations, counts, measurements, or responses.
    • Examples:
      • The eye color of students in a classroom (e.g., green, brown, blue).
      • The number of cars passing through an intersection in one hour.
      • A person's weight.
      • Customers rating their satisfaction on a scale from 1 to 5.

  • Statistics

    • The systematic study of how to collect, organize, analyze, and interpret numerical information derived from data.

  • Example: Applying the Statistical Process

    • Goal: To determine which gender in a class has the higher average age.
    • Collect: Record the ages of each individual (student) in the class.
    • Organize: Separate the recorded ages into two groups: one for males and one for females.
    • Analyze: Calculate the average age for the male group and the average age for the female group independently.
    • Interpret: Compare the two computed averages to conclude which gender has the higher average age.

  • Individuals and Variables

    • Individuals: The specific people or objects that are included in a study.
    • Variable: A distinct characteristic of an individual that is measured or observed.
    • Example 1: Laptop Reaction Time
      • Objective: Examine the reaction time of all laptops in a classroom when opening the Zoom application.
      • Individuals: The laptops (each specific laptop).
      • Variable: Reaction time (the time it takes for the Zoom application to open on each laptop).
    • Example 2: Student Characteristics
      • Individuals: Students.
      • Variables (characteristics): Major, Exam Score, Grade.
      • Data for Individual #3: Major = communications, Exam score = 82, Grade = ext{B}.

Types of Variables

Variables are categorized based on the nature of the information they represent.

  • Qualitative (Categorical) Variable

    • Classifies individuals into distinct categories or groups.
    • Examples:
      • A person's gender: Qualitative (categories are “male” and “female”).
      • The color of a car: Qualitative (categories are different colors like red, blue, black).
      • Check Your Understanding:
        • The model of car last sold by a particular car dealer: Qualitative.
        • The name of your favorite song: Qualitative.

  • Quantitative Variable

    • Has a numerical value or measurement, indicating