1. LSP 120 Quantitative Reasoning
Absolute vs. Relative
Quantities

2. Absolute vs. Relative
Absolute quantities are simply counts or totals of some type of data
Examples:
Number of highway deaths per year per state
Number of students in this class that earn an A
Number of adults with HIV per country

3. Absolute vs. Relative
While absolute quantities can provide some information, it is often incomplete or simply misleading
With relative quantities, the data is always “compared” to something.

4. Absolute vs. Relative Examples:
Number of highway deaths per year per state relative to the number of drivers per state
The percentage of students in this class that earn an A
The number of adults with HIV per country relative to the country’s population

5. Absolute vs. Relative Percentage and rate identify relative quantities
Average, mean, median… don’t automatically identify relative quantities unless they are averages/means/medians of relative values

6. Rates
What is a rate?
When you compare some value to a fixed number of another value
For example, highway deaths per 100 travelers
Infant mortality rates – deaths per 1000 babies born
For example
deaths per birth hard to comprehend
0.037 deaths per 10 births better
0.37 deaths per 100 births better still
3.7 deaths per 1000 births even better

7. Example of a Rate
The average number of people killed each year in hot-air balloon accidents is 2.6
The average number killed in hunting accidents is 600
Which is more dangerous?

8. Answer
There are two million hunters in the U.S. and just 3,000 hot-air balloonists
Balooning: 2.6/3000 =
Hunting: 600/2,000,000 =
Ballooning is approximately 3 times as more dangerous as that of hunting!

9. Confusion Which is safer – flying or driving?
Compare number of deaths killed each year in airplanes versus number killed on the highway?
Or is it more accurate to compare number killed in each per mile traveled?
Or is it more accurate to compare number killed in each per trip?

10. More Data Let’s take a look at another example:
HIV_Adults_By_Country_2001.xls
(start by going to
We’ll do some sorting, change the absolute values to relative, resort, then create a map using the QRC mapping tool