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)