Absolute and Relative Quantities

Week 4

The European Commission has just announced an agreement whereby English will be the official language of the European Union rather than German, which was the other possibility.

As part of the negotiations, the British Government conceded that English spelling had some room for improvement and has accepted a 5- year phase-in plan that would become known as "Euro-English".

In the first year, "s" will replace the soft "c". Sertainly, this will make the sivil servants jump with joy. The hard "c" will be dropped in favour of "k". This should klear up konfusion, and keyboards kan have one less letter. There will be growing publik enthusiasm in the sekond year when the troublesome "ph" will be replaced with "f". This will make words like fotograf 20% shorter.

In the 3rd year, publik akseptanse of the new spelling kan be expekted to reach the stage where more komplikated changes are possible.

Governments will enkourage the removal of double letters which have always ben a deterent to akurate speling.

Also, al wil agre that the horibl mes of the silent "e" in the languag is disgrasful and it should go away.

By the 4th yer people wil be reseptiv to steps such as replasing "th" with "z" and "w" with "v".

During ze fifz yer, ze unesesary "o" kan be dropd from vords kontaining "ou" and after ziz fifz yer, ve vil hav a reil sensi bl rite styl.

Zer vil be no mor trubl or difikultis and evrivun vil find it ezi tu understand ech oza. Ze drem of a united urop vil finali kum tru.

Und efter ze fifz yer, ve vil al be speking German like zey vunted in ze forst plas.

Make sense of this:

There are 10 kinds of people. Those who know binary and those who don’t.

It occurs once in a minute, twice in a week,

and once in a year. What is it?

Review Question

• You buy a new car for $22,500. The value of the car decreases by 25% each year. – What is the value of the car after three years?

y = 22500 * (1-.25)3 = $9492.19

– In how many years is the car worth $5300?Use Excel.

Review Questions

Absolute and Relative Quantities

Week 4

absolute vs. relative quantities

• Absolute: e.g.– count

• Relative: e.g.– rate (x out of y). Usually:

• 1 out of …• … out of 10 or 100 or 1,000 or 10,000

– percentage (%). Always out of 100

absolute vs. relative quantities

• Number of Hispanic students at Lane– 1670

• Number of Hispanic students at Juarez– 1471

• Percentage of Hispanic students at Lane– 40% (total 4248 students)

• Percentage of Hispanic students at Juarez– 94% (total 1565 students)

absolute vs. relative quantities• 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

Example: HIV count in 2005

Example: HIV count in 2005

• Order it by the number of infected people– Reorder them by the column of your choice – in

this case, column B

Example: HIV count in 2005

Example: HIV count in 2005

What three countries have the highest number of people living with HIV?

1. India2. South Africa3. Nigeria

Example: HIV count in 2005

• The list will be very different if ordered by relative values.

• Make a column of the percent of people living with HIV.– Change the format of the cell so that it shows

percentages.• Sort by the percent of people of living with

HIV. (Don’t forget to choose all the columns)

Example: HIV count in 2005

What three countries have the highest percent of people living with HIV?

1. Swaziland2. Botswana3. Lesotho

Example: HIV count in 2005

How do these countries rank in percentage?

1. India (57)2. South Africa (6)3. Nigeria (19)

Example: HIV count in 2005

• How many countries have 20% or more of its people living with HIV?

– 3 countries

Example: Using the maptool

• Open StatePopulation2000.xls

• Go to http://qrc.depaul.edu/maptool• Use copy/paste to make:

– a map of 1970’s population.– a map of 2000’s population.

• Make sure not to include any blank rows in the beginning, middle or after

Rate ProblemIn 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.”

Rate Problem• a. What is the rate of death for ballooning? What

is the rate of death for hunting?– .000867 (read 8.67 out of every 10,000); .0003

(3 out of every10,000)• b. Is 30, in the phrase 30 times as high, a relative

or absolute number? – relative

• c. Vlahos claims that the ballooning's death rate is 30 times as high as that of hunting. Do you agree? – .000867/.0003 = 2.89

be careful!

• Percent of• Percent More Than• Percent Less Than• Percent Increase• Percent Decrease

percentage problems

• Everything comes from this equation (from 2 weeks ago) …

Final Value (or New)

Initial value (or Old) Percent increase (or Times More Than) or Percent decrease (or Times Less Than)

Percent of (or Times as Much)

If you’re looking directly for a percent

For percent of do N/O AKA part/whole

For percent change (more or less) do (N-O)/O

percentage problems

• Tip: write the equation as you read it– “of” means x– “is” means =– “%” indicates you have to move your decimal

place by two to the left

percentage problems

• 2 is what percentage of 10?2 = x*10x = 0.2 = 20%

• 20% of what number is 2?0.2 * x = 2x = 10

• What is 20% of 10?x = 0.2 * 10x = 2

percentage problems

• 17 is 32% of what number?17 = 0.32 * xx = 53.125

• 67.2 is what percentage of 150? 67.2 = x * 150x = .448 = 44.8%

• What is 233% of 71?x = 2.33 * 71x = 165.43

percentage problems

• In Chicago in the year 2000, there were approximately 1.053 million African Americans, 907 thousand whites (non-Hispanic), and 754 thousand Hispanics, and 181 thousand others (other races or two or more races). What percentage of Chicagoans in 2000 were of Hispanic origin?total = 2.895 million% Hispanics = .754 / 2.895 = .2604 = 26.04%

percentage problems

• DePaul’s undergraduate student body is approximately 21,000 students. 54% of the student body is female. Approximate how many females attend DePaul?21000 * 0.54 = 11340

percentage problems

• In 1993, 248.7 million people in the United States were born in the United States, and the rest, 19.8 million were foreign born. What percentage of the total population of the US was foreign born?total population = 248.7 + 19.8 = 268.5% foreign born = 19.8/268.5 = .0737 = 7.37%

percentage problems

• The sales tax in Chicago for all non-perishable goods is 10.25%. The cashier rings up your purchase and tells you that your total bill is $103. What was the amount of your bill before taxes were added?103 = (1+.1025) * xx = 103/1.1025 = $93.42

percentage problems

• You are in another state (not Illinois). You are buying a computer at Best Buy. The price before taxes is $949. When the cashier wrings up your purchase you owe $1005.94. What is the sales tax in this state?949 * (1+x) = 1005.941+x = 1.06x = 0.06 = 6%

couple of more percent problems

• Chicago’s population grew from 2.78 million in 1990 to 2.90 million in 2000. By how many percent did it grow?

Answer: (2.90-2.78)/2.78=0.043=4.3%

• The life expectancy in Canada is 79.1 years; the life expectancy in the US is 76.0 years. By how many percent is the life expectancy of Canada higher than the life expectancy in the US?

Answer: (79.1-76.0)/76.0=0.041=4.1%

• How many times as large is the life expectancy of Canada than the life expectancy in the US?

Answer: 79.1/76=1.041 times as large

• By how many percent is the life expectancy of people in the US lower than the life expectancy in Canada?Answer: (76.0-79.1)/79.1=-0.039=-3.9%

• According to the official 2000 census, the Hispanic population of the US in 2000 was 35,305,818. It rose by an astounding 57.9% from 1990 to 2000. What was the Hispanic population in 1990?x*(1 + .579)= 35,305,818x = 35,305,818/1.579x= 22,359,606

• activities 5 & 6 today• assignment 4 for homework• Study for the midterm

– Practice midterm will be posted.– You are allowed one 3 by 4 index card of notes.