Strategies for Using the Aggregated Census Data
The data reported in the U.S. census tables are raw numbers. In most cases, it is misleading to use raw data to directly compare localities, states, or regions because of their differing physical sizes and populations. The measures defined below allow you to make comparisons between Augusta and Franklin Counties, and their respective states and regions, by converting the raw data to figures, which control for the different sizes of the population in these areas.
Proportions and Percentages
If you tell a friend that in 1860 there were 5616 slaves in Augusta County, your friend would probably reply, "Out of how many people?" By itself, the number 5616 is not very informative. It means one thing if there were only 6000 people in Augusta County. It means quite another if there were 27749, as reported by the 1860 U.S. Census. One way to make raw census data more meaningful is to express variables as a proportion or percentage of their total number.
Proportions, which take the form of fractions or decimal values, vary between 0 and 1. The formula to calculate a proportion is:
(number in a given category/total number)
Percentages are more frequently used to analyze census data than proportions. Percentages can be obtained from proportions by simply multiplying by 100. Their value varies between 0 and 100. The formula to calculate a percentage is:
(number in a given category/total number) * 100
Applying this formula to our example: (5616 slaves/27749 total people)*100=20.2. Thus, we can say that slaves accounted for 20.2 percent of Augusta County's total population. This gives us a much better feel for the density of the slave population in Augusta County than our original figure of 5616 slaves. Because percentages standardize for population size (the word "per cent" actually means "per hundred"—we are calculating the number of slaves per hundred people) we can also use this figure to compare Augusta County with Virginia, or the South as a whole, when similar figures are computed for those regions.
Percentages are most often used to express a variable in terms of that variable's total number (for example, slaves formed 20.2 percent of the total population of Augusta County in 1860). Ratios can be used in cases where the variables being compared represent separate and distinct categories. For example, in order to get a sense of the relative size of each group, one could compute the ratio of students to teachers in the Franklin County public schools in 1850.
The formula for calculating the ratio of variable A to variable B is: (A/B)
Note that, unlike a proportion, a ratio can take on a value greater than one. According to the 1850 census there were 8579 pupils in the Franklin County public schools and 177 teachers. Hence, the ratio of students to teachers was (8579/177) or 48.4. For every teacher, there were, on average, 48.4 students! This can also be written as 48.4:1. Because ratios standardize for population size (we are calculating the number of students per 1 teacher), we can compare the student-teacher ration in Franklin with that of Augusta when a similar figure is computed for that county.
Ratios as computed above are expressed in terms of a base denominator of 1 (the number of students per 1 teacher). However, ratios can be expressed in terms of any base number that you choose by simply multiplying the ratio by that base. Sex ratios, for example, are usually presented in terms of the number of males per 100 females. If we calculate the ratio of white males to white females in Augusta County in 1860 (10880/10667=1.019), and then multiply that number by the base 100 (1.019 * 100=101.9=102), we find that the sex ratio among whites in Augusta County was 102. This indicates that the white male and white female populations in Augusta County were relatively balanced--for every 100 white females there were 102 white males. The sex ratio among Augusta County's slaves, on the other hand, was 203, signifying that there were more than twice as many male slaves as female slaves. Once again, because ratios standardize for population size, we can use this figure to compare the sex ratio of Augusta County's slave population with that for Virginia, or the South as a whole, when similar figures are computed for those regions.
Rates are a special type of ratio. Large base numbers such as 1000 or 100000 are often used to compute rates whenever the use of proportions or percentages would result in very small decimal numbers. Murder rates, for example, are often expressed in terms of the number of murders per 100,000 population.
Rates of Increase
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:
((year 2 - year 1)/year 1)
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.