Oftentimes we want to know if a characteristic of the population has changed over time, and at what rate. For example, how fast, if at all, was the free black population in Augusta County growing between 1850 and 1860? How did this compare to the rate of increase for the free black population in Franklin County?
The formula to calculate a rate of increase for any given variable between year 1 and year 2 is:
Note that if the value for year 2 is less than the value for year 1, the rate of increase will be negative (and can properly be termed a rate of decrease). Rates of increase can be transformed into percentage rates of increase by simply multiplying by 100.
To follow through with our example, according to the U.S. censuses, the free black population of Augusta County increased from 574 in 1850 to 586 in 1860. Subtracting the 1860 value from the 1850 figure results in a positive increase of 12 free blacks. Dividing this difference by 574 (the free black population in year 1) yields a rate of increase of .02. Multiplying this rate by 100 to form a percentage, we can say that the number of free blacks in Augusta County increased two percent between 1850 and 1860. Because rates of increase standardize for population size, we can compare this figure to rates computed for Franklin county, different states or regions, or the U.S. as a whole. The comparable rate of increase for Franklin County, for example, was -.076. This indicates that the free black population in Franklin County actually declined 7.6 percent between 1850 and 1860.