Worksheet 3 Absolute and Relative Quantities

1. In the August issue of Popular Science James Vlahos wrote:

Risk assessors rip their hair out at the general public’s innumeracy; many people jump to conclusions based only on absolute numbers and don’t consider ratios as well. For example, the average number of people killed each year in hot-air balloon accidents is 2.6, while the number killed in hunting accidents is 600. But there are two million hunters in the U.S. and just 3,000 hot-air balloonists, which makes ballooning’s death rate 30 times as high as that of hunting.

 a. What does Vlahos mean by innumeracy?

b. What is the rate of death for ballooning? What is the rate of death for hunting?

c. Is 30, in the phrase 30 times as high, a relative or absolute number?

d. Vlahos claims that the ballooning's death rate is 30 times as high as that of hunting.  Do you agree?  (in other words using your answers from b do the calculation yourself)

2.  Two and a Half Men.  The show is about two brothers, Charlie (makes good money and likes to spend it) and Alan (very responsible), who have their hands full raising Alan’s teenaged son Jake.

In a recent episode, Charlie runs low on cash and ends up having to change his ways (just temporarily).  At the beginning of the show, Charlie is throwing around his money, as he always does.  When the pizza delivery person comes to deliver a pizza, Charlie gives him $50 and tells him to keep the change.  Alan, who knows Charlie is temporarily broke, exclaims "You just gave him a 300% tip".

a.  Based on this information, how much was the pizza?

b.  Later in the episode, Alan stops Charlie from tipping so much and suggests that Charlie give only a 20% tip.  Charlie gives the  pizza delivery person only $2.50.  (Of course the delivery person tells Charlie he will no longer be delivering pizza's to his home.)  Based on this information, how much was the pizza?

c.  Did the writers portray a realistic scenario?  Explain.

3. Which of the following statements refer to relative quantities and which refer to absolute quantities?

a. the 2004 freshman class at DePaul was 2,317 students

b. more than half of the students at DePaul are women 

c. the death toll from Hurricane Katrina might reach 10,000

d. the ratio of females to males at DePaul is 1.4

e. a couple has a 20% chance of conceiving a child during any given month

f. DePaul students come from 45 states and territories; 75% are from Illinois

g. one out of every 10 people are left-handed

h. Athens spent 5 times more than Sydney on Olympic security