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2.2.3. Discrete vs. Continuous Probability Distributions
A continuous probability distribution is composed of continuous variables, as opposed to a discrete probability
distribution, which is composed of discrete variables. Other differences between the two types of distributions
also exist.
Consider the following graph of men’s heights probability distribution:
50
Probability
30
50% 50%
10
60 70 80
Height (Inches)
The probability, that a particular random variable will equal a certain value, is zero. For example, let’s say you had
a continuous probability distribution for men’s heights. What is the probability that a man will have a height of
exactly 70 inches? The chart shows that the average man has a height of 70 inches (50% of the area of the curve is
to the left of 70, and 50% is to the right). But it’s impossible to figure out the probability of any one man measuring
exactly 70 inches. Why not? Imagine measuring a man who is 70 inches tall. It’s unlikely that he’s exactly 70 inches.
He’s probably 70.1 inches, or perhaps 69.97 inches. And it doesn’t stop there. He could be 70.1045 inches, or
69.9795589 inches. The fact is, it’s impossible to exactly measure any variable that’s on a continuous scale, and
so it’s impossible to figure out the probability of one exact measurement occurring in a continuous probability
distribution.
2.3. STATISTICAL PROBLEM-SOLVING PROCESS
To gather and analyse data in order to respond to statistical inquiry questions is the goal of the statistical problem
solving process. Each of the four components of this investigative method involves examining and addressing
variability:
Step
by
Step Target
Interpret the
Data
Analyse the
Data
Collect/consider
the data
Plan: Formulate
Standard Investigative
Questions
Distributions in Data Science 145

