Introduction to Statistics Concepts

Jan 29, 2025

Statistics Lecture Notes

Definition of Statistics

  • Statistics: The collection and interpretation of data.
  • Used to measure and analyze variability (heights, weights, hair color, etc.).

Types of Statistics

  1. Inferential Statistics
    • Involves analyzing a sample to make judgments about a population.
  2. Descriptive Statistics
    • Involves summarizing data and describing it (e.g., average midterm score).
    • Tools: Histograms, graphs.

Course Structure

  • First part: Descriptive statistics.
  • Second part: Inferential statistics.

Basic Definitions

  • Population: Total amount of items (people, cats, vehicles).
  • Sample: A small part of the population used for study.
  • Sample Size: The number of items in a sample.

Variables

  • Variable: Characteristic of what is being studied (measurable, countable, categorizable).
    • Examples: Height, weight, hair color.
  • Types of Variables:
    • Quantitative Variables
      • Measured in numbers, suitable for arithmetic calculations (e.g., average).
      • Examples: Height, weight, midterm score.
    • Categorical Variables
      • Values that place things into groups or categories.
      • Examples: Hair color, type of cat, letter grade.

Types of Categorical Variables

  1. Ordinal
    • Logical ordering of values (e.g., letter grades).
  2. Nominal
    • No logical ordering (e.g., hair color).

Types of Quantitative Variables

  1. Discrete Variables
    • Measurable in certain numbers (e.g., number of pets).
  2. Continuous Variables
    • Can take any numerical value (e.g., weight).

Recap

  • Population: Total number of items.
  • Sample: Part of the population examined.
  • Sample Size: Number in a sample.
  • Variable of Interest: What is measured from each individual.
  • Data Types:
    • Quantitative (e.g., midterm scores)
    • Categorical (e.g., letter grades)