Motivator:

I recently got a question from a colleague wondering what the difference is between growth rate and percent change. Understanding concepts like these help us understand what’s going on among Oregon’s people, places, and society, so here’s a post that deals a bit with the technical details of demographic measurement.

The Nugget:

Percent change represents the relative change in size between populations across a time period. Growth rate represents the average amount of change per year or per month across a time period.

Two Examples to Illustrate:

Today we’ll use change in 1) the population age 18-34 and 2) the Latino population in Oregon, 1990 to 2010, as examples to illustrate the difference between growth rates and percent change.

This chart clearly shows that both populations have grown over the last 20 years, but how much have they grown? How can we talk about their rates of change and the magnitude of increases? Calculating percent change and growth rates allow us to do both.

Percent change represents the relative change in size between populations across a time period. The formula is:

So in our example, the Latino community in Oregon grew 273% between 1990 and 2010, because there was an absolute increase in the population from 112,707 to 420,195 people. I calculated that by taking 420,195 – 112,707 = 307,488 and dividing that by 112,707 to equal 2.73. Which, when multiplied by 100 to create the percentage, yields 273%.

The Oregon population age 18-34 grew 30% between 1990 and 2010, from 678,677 to 882,922 people. That’s 882,922 – 678,677 = 204,245, divided by 678,677, which is .3; 30%.

Growth rates are trickier and not everyone uses the term the way they are supposed to (even I sometimes get sloppy with the terms!). Often people use the term “growth rate” when they mean percent change, but technically a growth rate is the average amount of change per year or per month across a longer period. There are lots of formulas for calculating growth rates because there are different assumptions you can apply to the data – like assuming the growth rate in the period was linear, or exponential, or geometric. But if we assume linear growth, the formula for the annual growth rate is:

So, in our example the annual growth rate of the Latino population between 1990 and 2010 was: 13.64%, because 420,195 (people in 2010) – 112,707 (people in 1990) = 307,488 and 307,488/20 years = 15,374.4. Which divided by 112,707 (people in 1990) = .1364; equivalent to 13.64%.

And the annual growth rate of young adults age 18-34 between 1990 and 2010 was 1.5%. As this formula shows:

Important to note is the fact that neither the growth rates nor the percent changes were equal in the two decades for either population.

As the tables show, there were higher percentage increases and greater rates of growth among both these populations in the 1990s than in the 2000s. This illustrates the importance of breaking down time intervals of change into the smallest measureable units so you can see the way growth and change fluctuate over time.

The Take-Aways: