1.2 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
- IMSE 440 Applied Statistical Models in Engineering
- Offered in Winter semesters