Database Reference
In-Depth Information
Chapter 4. Ratios and Rates
“We are the safest large city in America, but any crime rate is too high.”
—Michael Bloomberg, former mayor of New York City
Until now, we've considered absolute amounts of countable and measurable nouns, like pop-
ulation, tons of garbage collected, and number of rat sightings by borough. Pleasant, I know.
areas and different numbers of people living in them. The fact that they produce different
amounts of garbage isn't surprising, and probably doesn't make for a very interesting mes-
sage to communicate to an audience.
These absolute comparisons, while helpful for showing the big picture, aren't generally con-
sidered “apples-to-apples” comparisons. There are apples, and, well, there are Big Apples.
A helpful way to “normalize” comparisons is using ratios, rates, proportions, and percent-
ages. What's the difference between these four?
▪ A
ratio
is a comparison of two terms expressed as a quotient. For example, Manhattan
produced 0.264 tons of recycle for every ton of refuse. Ratios can be expressed as “x to
y,” “x:y,” “x/y,” or as a decimal.
▪ A
rate
is a ratio in which the two terms have different units. For example, the population
density of Brooklyn is 36,136 residents per square mile. Rates are often predictive be-
cause time can be used as the denominator (crime rates, population growth rates, etc.).
▪ A
proportion
is a ratio in which the numerator is a partial amount and the denominator is
the total amount (expressed as a number between 0 and 1). For example, the proportion
of the NYC population living in the Bronx is 0.169. A proportion is expressed as a num-
ber between 0 and 1.
▪ A
percentage
is a ratio comparing a number to 100. For example, 16.9% of NYC resid-
ents live in the Bronx. A percentage is generally a number between 0 and 100, but can be
larger than 100 (e.g., “sales have increased by 150% year-over-year”).