Population, sample, and variable

Population

  • Definition: A collection of objects of interest in a study
  • Studying who will win an upcoming mayoral election
    • Population: Everyone who are planning to vote
  • Studying the defect rate of a cellphone screen from a manufacturer
    • Population: All the cellphone screens made by the manufacturer

Sample

  • Definition: A subset of the population selected by a defined procedure
  • Studying who will win an upcoming mayoral election
    • Sample: An telephone poll of 500 randomly selected potential voters
  • Studying the defect rate of a cellphone screen from a manufacturer
    • Sample: 200 randomly selected screens for inspection

Variable

  • Definition: A characteristic of interest for the elements
  • Houses
    • size, # of bedrooms, year built, school district, …
  • Patients
    • age, weight, blood sugar level, …
  • Universities
    • tuition, enrollment, graduation rate, …

Discrete variables

The variable takes finite or countably infinite values.

  • Toss a coin four times, the number of heads you get
  • The attendance to a basketball game
  • The number of orders that an online shop receives in a day

Continuous variables

The variable takes infinitely many, uncountable values.

  • The water level of dam
  • The speed of riding a bicycle
  • The time when an order arrives at a shop

If it can take on two particular real values, it can also take on all real values between them.

  • If you can count it, it is discrete.
  • If you need to measure it, it is continuous.

Univariate vs. multivariate

Univariate: A single variable

  • Battery life of a cellphone model
  • Blood sugar level of diabetic patients

This course focuses mostly on a single variable (except for Chapter 5. Joint Distributions).

Multivariate

Studying the relationship among two or more variables