Ratios: ratios are one number expressed in relation to another by dividing the one number
by the other. For example, the sex ratio of Delaware in 1990 was:
343,200 females to 322,968 males or 1.06
This can easily be expressed in terms of males to females, .94. There is really no way
other than tradition and practice or your specific purpose to determine which figure is the
numerator and which is the denominator. The interpretation of the sex ratio is that for every
male there are 1.06 females. Sometimes we express this as the ratio per 100, 1,000, or
100,000 persons. So, we could say 106 females for every 100 males.
Other ratios commonly used are:
Population Density -- the number of people per square mile. In 1990 in Delaware, the
population density was:
666,168 persons / 1955 sq. miles = 341 persons per square mile
In New Castle County, the population density was:
441,946/426 = 1,037 persons per square mile
The Dependency Ratio -- the number of people under age 15 plus the number 65 and over
divided by the number of people 15 to 64. It is a crude measure of dependency that
assumes age defines your economic contribution. :
In 1994 in Delaware, the dependency ratio was estimated as:
( 152,869+ 90,329)/462,396 = .53
For every 100 workers there are 53 dependents, or
For every dependent, there are 1.9 workers
2. Proportions: proportions are special kinds of ratios where the denominator is the total
while the numerator is a subpart of the total. This tells us what part the numerator is of the
total. Thus, while the ratio of females to males in Delaware is 1.06, females represent .515
proportion of the total. Percentages are just a form of the proportion based on 100 people.
To calculate a percentage we simply multiply a proportion by 100 (females are 51.5% of the
total).
3. Rates: rates are a special form of a ratio which represents the probability of a certain
event. The numerator is the number of occurrences of an event during a time period, and
the denominator is the number of persons exposed to that event in the time period. To be a
true rate we must try to have only those at risk in the denominator. Sometimes this is
difficult to do so we use approximations or use the total population. In the latter case we
generally call it a crude rate. Let’s use fertility rates as examples:
The Crude Birth Rate is given by the number of live births per 1,000 population in a given
year. In 1994 the crude birth rate for Delaware was estimated as:
(10,390/705,594) x 1,000 = 14.7
