LSP 120: Quantitative Reasoning and Technological Literacy

Section 118

Özlem Elgün

Housekeeping

• Midterm: October 18th, Monday in class– Midterm review and practice posted on the website– Review session, on October 13th , Wednesday, 7:30- 9:15 pm.

• Assignment 4 due October 20th, Wednesday

• Final Project introduction– Determining groups/topics– Stage 1 due October 20th Wednesday

Absolute and Relative Quantities

There are two ways to measure numerical data—particularly if the goal is to measure the least and greatest occurrence of some quantifiable variable.

• The absolute quantity is a measure of the absolute occurrence of the variable. It is a “sheer” number. It tells how many or how much. (number of adults who have HIV)

• The relative quantity is the absolute quantity divided by some other quantity. (percent of adults who have HIV)

Different types of Relative Quantities

Fraction or Percent:• Fractions or percents are used when comparing part to total of the same type of

variable. (example: percent of adults with AIDS/HIV) Percents can also be used to show the relative change. Percent change is calculated by dividing the absolute change by the original amount. [Reminder: Percent change (new value –old value)/old value]

Rate:• Rates are used compare different types of variables (example: tickets per person, miles

per hour, or crimes per 1000 people) Ratio:• Ratios are used to compare the same type of variable from two sources. For example:

California’s population is 33,872,000 and Oregon’s population is 3,421,000. Clearly CA’s population is larger but how many times larger? 33,872,000/3,421,000 = 9.90 Calculating the ratio of the populations tells us that CA’s population is almost 10 times as large as OR’s population.

• The type of data you have will determine what type of relative quantity is appropriate.

• We use absolute change to describe the actual increase or decrease from a reference (or old/earlier) value to a new (or later) value:

• Absolute Change = new value – reference value

• We use relative change to compare the absolute change to the reference value:

• Relative Change = =

Absolute and Relative Change

• For communication purposes, we convert relative change, which is a fraction (converted to a decimal number) to a percentage (percentage change). The following are three ways to convert a fraction (decimal number) to a percentage:

• Move the decimal place to the right two places• Multiply by 100%• Use the button in Excel

• For this course, we will generally show percentages formatted to two (2) decimal places. (Right click on the cell, format cell)

Examples:• During a 6-month period Nokia’s stock doubled in price from $10 to $20.

– Calculate the absolute, relative and percentage changes in the stock price.• Absolute change = $10• Relative change= 1 (Technically it is a fraction)• Percent change = 100%

– When a quantity doubles, what is its relative change? percentage change?• 100%

– Will you get the same answer if the stock started at $5 and doubled to $10? If a service fee doubled from $25 to $50?• Yes

• The number of DVD players in homes in the United States increased dramatically from 1999 to 2001, from 5.4 million to 25.1 million. By how many percent did it rise from 1999 to 2001?– 365%

• In 2001, there were 654 drive in theaters in the US, 77% fewer than in 1985. Approximately how many drive in theaters were there in 1985?– 2843

• Enrollment at DePaul University has grown by 36% from 1990 to 2001. If the Fall 2001 enrollment was 21,363 students then what was the total enrollment in 1990? – 15708

• The January 14, 2002 issue of Sports Illustrated reported that the average home attendance for the Washington Wizards in 2000-01 season was 16,075. Since Michael Jordan’s return as a NBA player, the average attendance at Wizards home games has grown to 20,874 for the 2001-02 season. What percent increase does this represent? – 29.85%

Map Tool

• Creating Maps using the Map Tool on the QRC website