Quantitative variables can be distinguished further into discrete and continuous quantitative variables. The difference lies in what values are possible.
Take the number of siblings you have. Options would be 0, 1, 2, 3, 4, and so on. Would any value in between be possible? Could you have 1.7 siblings? This would be ridiculous. This is an example of a discrete variable.
Now, take the weight of different people. Options would be 100 pounds, 101, 102, 103, 104, and so on. Would any value in between be possible? Could someone weight 103.76 pounds? Absolutely. This is an example of a continuous variable.
Discrete Quantitative Variables
Continuous Quantitative Variables
Can only be specific values
Incremental
Can be any value
Examples:
What year were you born? (2002, 2003, but not 2002.5)
How many pets do you have? (2, 3, but not 2.5)
How many credits is a class worth? (0.5, 1, 1.5, 2, 2.5, ..., but not 1.7)
Examples:
Temperature (32*F, 33*F, and any value between is possible)
Height (5'4", 5'5", and any value between is possible)
Age (32, 33, and any value between is possible)
We often only report whole numbers. You may be 25.347623 years old, but we would simply say "25 years old." This turns it into a discrete variable.
Practice
Following are the quantitative variables that we identified from lesson 1.1 along with a comple of other variables. Identify if these are discrete or continuous variables.
Age
After answering on your own, check the
Value of a house
After answering on your own, check the
GPA
After answering on your own, check the
Height
After answering on your own, check the
Number of books on your bookshelf
After answering on your own, check the
## Problem 1.2.1
Is "Age" a Discrete or Contiuous variable?
When you report your age, you often declare your age in whole years: "I am 22," or "I am 23". Sometimes even by half years: "I am 22 and a half."
However, your actual age is an exact number, like 22.482153 years old. So, age is often reported as a a discrete variable, but in actuality is a __continuous__ variable.
The true age really is continuous, but it just is reported as a continuous variable.
## Problem 1.2.2
Is the "Value of a house" a Discrete or Continuous variable?
The value of a house is reported in dollars. The value can have a decimal (the cents). However, it is limited to the hundredths of a dollar (the single cent). That is, a house can have a value of $123,456.78, but will never see three decimal places like $123,456.789.
So, the value of a house is a __discrete__ variable.
## Problem 1.2.3
Is a student's "GPA" a discrete or continuous variable?
A GPA is an average score based on performance in all classes. The average can have any number. So, the GPA is a __continuous__ variable.
*Note*: GPA on transcripts are often rounded to the hundredth. However, this is just a rounded number. The actual GPA is a long decimal. Here's an example:
* Grades for a semester are A(4.0), B(3.0), B+(3.5), A-(3.7), B+(3.5), A(4.0)
* The average grade is 3.616666666666... This is the true GPA.
* For simplicity, the GPA would be rounded to 3.62.
## Problem 1.2.4
Is a patient's "height" a discrete or continuous variable?
Height is often reported to the nearest inch. However, two people that are reported as 6 feet 2 inches tall are likely not exactly 6 feet 2 inches. There may be a slight different in height between the two patients.
So, this height would be a __continuous__ variable.
## Problem 1.2.5
Is the "Number of books on your bookshelf" a discrete or continuous variable?
If you are counting books, you will only have whole numbers of books (10, 13, 17, 22, ...). You won't have 14.63 books. Since it's a whole number, this would be a __discrete__ variable.