Discrete Variables

As mentioned before, there are two main categories of probability distributions: discrete probability distributions and continuous probability distributions. To see the difference, let's talk about discrete variables and continuous variables.

The word discrete implies that a variable can only take on certain values. Usually this ends up meaning that the variable is countable like:

• Number of times a coin landed on heads
• How many times a dice landed on 1, 2, 3, 4 5 or 6

You wouldn't say that a dice landed midway between 3 and 4 like 3.4. Or that the coin landed on heads and a half. And oftentimes these discrete variables lend themselves to counting like:

• How many times did the coin land on heads?
• How many times did the dice land on five?

Of course, in a real-world experiment, the coin has some tiny tiny chance of landing on its side or the dice on an edge. But the case would still be discrete; you'd create an category like "side" or "edge" to account for those cases.

Continuous Variables

In contrast, a variable like temperature is continuous. Temperature can take on any decimal value like -5.6 or 100.41 degrees.

Weight, height, temperature, longitude, and latitude are continuous variables. All of these variables could be decimal values. These variables have something else in common; you'd use some sort of instrument to measure them like a thermometer, a ruler, a scale or in the case of longitude, a chronometer.

Notice as well that you can't really associate counts with these variables. With a discrete variable like coins, you could count the number of times the coin landed on heads.

The probability distributions for discrete variables and continuous variables are different. In this lesson, you are going to learn the differences and similarities between the two.

QUIZ QUESTION::

Determine which situations would be discrete or continuous.

ANSWER CHOICES:

Hair color of students (brown, red, blond, etc)

Height rounded to the nearest integer

Altitude

Acceleration

Heads vs Tails for a Coin

Variable	Discrete or Continuous
Discrete
Discrete
Continuous
Discrete
Continuous
Continuous

SOLUTION:

Variable	Discrete or Continuous
Discrete	Hair color of students (brown, red, blond, etc)
Discrete	Height rounded to the nearest integer
Discrete	Heads vs Tails for a Coin
Discrete	Hair color of students (brown, red, blond, etc)
Discrete	Height rounded to the nearest integer
Discrete	Heads vs Tails for a Coin
Continuous	Altitude
Continuous	Acceleration
Discrete	Hair color of students (brown, red, blond, etc)
Discrete	Height rounded to the nearest integer
Discrete	Heads vs Tails for a Coin
Continuous	Altitude
Continuous	Acceleration
Continuous	Altitude
Continuous	Acceleration