Notes on Discrete vs Continuous Variables (Chapters 1–2)

mục tiêu: learn how to distinguish between discrete and continuous variables.
guiding rule: typically, a variable is discrete if its value results from counting, while a variable is continuous if its value is measured.
objective of this chapter: determine whether the quantitative variables described are discrete or continuous.
examples introduced in this chapter:
- The number of heads obtained after flipping a coin five times.
- The number of cars that arrive at a McDonald’s drive-thru between twelve and 1 PM.
- The distance a 2,011 Toyota Prius can travel in city driving conditions with a full tank of gas.
Example 1: Number of heads after flipping a coin five times
- This variable is discrete.
- There are a finite number of values the variable can take: 0, 1, 2, 3, 4, or 5.
- The value is obtained by counting the number of heads.
- possible outcomes (by counting): ${0,1,2,3,4,5}$
Example 2: Number of cars arriving at a McDonald’s drive-thru between twelve and 1 PM
- This variable is discrete because we count the number of cars that arrive.
- Possible values include 0, 1, 2, 3, … (and so on).
Summary for Chapter 1
- Discrete variables arise from counting; they have a finite or countably infinite set of values.
- The underlying method is counting the number of discrete events.

example: the distance the 2,011 Toyota Prius can travel in city driving conditions with a full tank of gas
- This variable is continuous because it is measured.
- measurement units mentioned: miles, feet, etc.
key distinction: continuous variables are obtained by measurement rather than by counting, and they can take on an infinite number of values within a given range
concluding note: in this transcript, the distance example demonstrates a measurement-based, continuous variable in contrast to the counting-based discrete examples in Chapter 1