Absolute and Relative Quantities

There are two ways to measure numerical data.

Absolute Quantities

An absolute quantity is a count or simple measurement. It tells how many or how much. For example, the excel file HIV_Adults_By_Country_2016.xlsx contains data the number of adults with HIV in countries around the world. One could reorganize the data by sorting adults with HIV in descending order. (To sort, click on a cell in the column you wish to sort by then click on the sort descending icon on the toolbar.) One would find that South Africa, India, and Nigeria have the highest number of adults with HIV. However, one cannot necessarily conclude that these countries have the worst problem with HIV since there are vastly different populations. Another way to look at the data would be with relative quantities.

Relative Quantities

A relative quantity is generally an absolute quantity divided by some other quantity.

For example, in the previous excel file, one could calculate the percent of the adult population infected with HIV by dividing the number of adults with HIV by the total adult population of the country. If that calculation was done and that column was sorted, Botswana, Lesotho, and Zimbabwe have the highest percents.

This is a very different picture. Which is more informative? It depends on what question you are attempting to answer. How and why did certain countries move when sorting by absolute quantity (number of infected adults) vs. relative quantity (percent of adults with HIV)?

India which had the second highest number of infected adults also has the second highest adult population in the world so in some ways it is not surprising that it has a high number of adults with HIV. Once the population is taken account by calculating the percent, India drops down the list since only 1% of its population is infected. The high absolute quantity yielded a low relative quantity because the number you divided by (the total adult population) was so large. South Africa had the highest number of infected adults and also had a fairly high percentage because its total population is not that large.

Usually when dealing with state or country information, a relative quantity is more informative because it allows you to compare states or countries to each other. By calculating the relative quantity, you are taking the differing populations of the country into account.

Examples 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.

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 California'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 California's population is almost 10 times as large as Oregon's population. The type of data you have will determine what type of relative quantity is appropriate.

Practice: 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