LSP 120 QUANTITATIVE REASONING Absolute vs Relative Quantities

LSP 120 QUANTITATIVE REASONING Absolute vs. Relative Quantities

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

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.

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

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

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 0. 0037 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

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?

ANSWER There are two million hunters in the U. S. and just 3, 000 hot-air balloonists Balooning: 2. 6/3000 = 0. 000867 Hunting: 600/2, 000 = 0. 0003 Ballooning is approximately 3 times as more dangerous as that of hunting!

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?

MORE DATA Let’s take a look at another example: HIV_Adults_By_Country_2001. xls (start by going to http: //qrc. depaul. edu) We’ll do some sorting, change the absolute values to relative, resort, then create a map using the QRC mapping tool