Geoscience Reference
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EXAMPLE 8.2A
Problem: A city of 4,000,000 persons has 500 clinics. Calculate the ratio of clinics per person.
Solution:
(500/4,000,000) × 10 n = 0.000125 clinics per person
To get a more easily understood result, we could set 10 n = 10 4 = 10,000. Then the ratio becomes:
(0.000125) × 10,000 = 1.25 clinics per 10,000 persons
We could also divide each value by 1.25 and express this ratio as 1 clinic for every 8000 persons.
EXAMPLE 8.2B
Problem : Delaware's infant mortality rate in 2001 was 10.7 per 1000 live births (Arias et al., 2003).
New Hampshire's infant mortality rate in 2001 was 3.8 per 1000 live births. Calculate the ratio of
the infant mortality rate in Delaware to that in New Hampshire.
Solution:
(10.7/3.8) × 1 = 2.8:1
Thus, Delaware's infant mortality rate was 2.8 times as high as New Hampshire's infant mortality
rate in 2001.
8.2.1.2 A Common Environmental Health Ratio: Death-to-Case Ratio
Death-to-case ratio is the number of deaths attributed to a particular disease during a specified
period divided by the number of new cases of that disease identified during the same period. It is
used as a measure of the severity of illness. The death-to-case ratio for rabies is close to 1 (that is,
almost everyone who develops rabies dies from it), whereas the death-to-case ratio for the common
cold is close to 0. In the United States in 2002, for example, a total of 15,075 new cases of tuber-
culosis were reported (CDC, 2004). During the same year, 802 deaths were attributed to tubercu-
losis. The tuberculosis death-to-case ratio for 2002 can be calculated as 802/15,075. Dividing both
numerator and denominator by the numerator yields 1 death per 18.8 new cases. Dividing both
numerator and denominator by the denominator (and multiplying by 10 n = 100) yields 5.3 deaths per
100 new cases. Both expressions are correct. Note that, presumably, many of those who died had
initially contracted tuberculosis years earlier. Thus, many of the 802 in the numerator are not among
the 15,075 in the denominator; therefore, the death-to-case ratio is a ratio, but not a proportion.
8.2.2 p roportion
A proportion is the comparison of a part to the whole. It is a type of ratio in which the numerator is
included in the denominator. We might use a proportion to describe what fraction of clinic patients
tested positive for HIV, or what percentage of the population is younger than 25 years of age. A
proportion may be expressed as a decimal, a fraction, or a percentage. The method for calculating
a proportion is
Number of persons or events with aparticular characteristic
Total numberofpersons orrevents, of whichthe numerator is asubset
×10 n
Two examples of proportions are
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