ISP 120 Class Notes

### Absolute versus Relative Change

There are two ways to measure change in numerical data.  One can examine either the absolute change or the relative change.

The absolute change in numerical data is the difference between the initial and final figures.  That is, the final amount minus the initial amount.  If the absolute change is negative, this implies a decrease from the initial to the final amount. If the absolute change is positive, this implies an increase from the initial to the final amount.

The relative change in numerical data is the ratio of the absolute change relative to the initial amount.  That is, the absolute change divided by the initial amount. Typically, this ratio is then converted to a percentage change.

In fact, percentage change and relative change are synonymous.  If the relative change is negative, this implies a percent decrease from the initial to the final amount. If the relative change is positive, this implies a percent increase from the initial to the final amount.

To study the distinction between these two different ways of measuring change, refer to the EXCEL file WorldCountryPop.xls, which lists the population of various countries in the world in 1980, 1990, and 2000. If we measure the population change of the countries from 1990 to 2000 using the absolute change, we can see which country experienced the greatest and least population change.

Notice that the Ukraine experienced the greatest decrease in its population from 1990 to 2000.  It lost 2,505,000

people.  In contrast, India experienced the greatest increase in its population from 1990 to 2000.  It gained 163,446,000 people.   Note: Pay close attention to the population figures which are given in thousands.

 Area Population (in thousands) Country or area (sq. mile) 1980 1990 2000 Absolute Popul Change from 1990 to 2000 Ukraine 233089 50047 51658 49153 -2505 Russia 6592817 139045 148082 146001 -2081 Bulgaria 42683 8844 8894 7797 -1097 Bosnia and Herzegovina 19741 4092 4424 3836 -588

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 Nigeria 351649 69593 92483 123338 30855 Indonesia 705189 154936 188651 224784 36133 China 3600930 984736 1138895 1261832 122937 India 1147950 690462 850558 1014004 163446

One can measure the population change of these countries in relative terms, also.  This can be especially informative since the 1990 populations vary so much from country to country.  We can measure what percent of the initial (1990) population the absolute change represents.  That is, we want to form the ratio between the absolute population change and the initial (1990) population for each country.  To do this, we divide the absolute population change by the initial (1990) population to find the relative population change from 1990 to 2000.

Notice below, that Bosnia-Herzegovina experienced the greatest percent decrease in its population.  A loss of 588 thousand people reflects a 13.29% decrease in its initial (1990) population.  In contrast, Afghanistan experienced the greatest percent increase in its population.  Its 2000 population is 75.52% greater than its initial (1990) population.

 Area Population ( in thousands) Country or area (sq. mile) 1980 1990 2000 Absolute Popul. Change from 1990 to 2000 Relative Popul. Change from 1990 to 2000 Bosnia and Herzegovina 19741 4092 4424 3836 -588 -13.29% Bulgaria 42683 8844 8894 7797 -1097 -12.33% Latvia 24903 2525 2672 2405 -267 -9.99% Estonia 17413 1482 1573 1431 -142 -9.03%

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 French Guiana 34421 68 116 173 57 49.14% Jordan 35344 2163 3262 4999 1737 53.25% Qatar 4247 231 481 744 263 54.68% Afghanistan 250000 14985 14750 25889 11139 75.52%

Although we can measure change in numerical data in two ways, it is generally more informative to calculate the relative change because it a quantitative measurement that is very sensitive to what the initial amount is (which is the denominator in the ratio).  Think about this claim by looking at the first table above where Bulgaria experienced a smaller absolute loss in its population than Russia did.  However, because Bulgaria’s initial (1990) population is so much smaller than Russia’s, the relative population change for Bulgaria is a whopping 12.33% population loss.  Whereas, Russia’s percent decrease in population is only 1.4%.

Here is another look—using a more graphical approach—at the very different conclusions that can be reached when measuring numerical change according to absolute versus relative terms.  Carefully compare and contrast the geographical trends of the absolute population change versus the relative population change.  There are some dramatic differences to be observed here which once again highlight the distinction between the quantitative measurements of absolute change and relative change.