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## October 7, 2014

### Rates help us compare

This is the second of two posts on basic math.

Use rates when you want compare something in groups of different sizes.

Say New York City has 400 homicides a year. Say Baltimore City has 300 homicides. Is New York more dangerous than Baltimore because New York has more homicides. No. Because New York is much larger. But the homicide numbers don't tell us that. Rates take different population sizes into account.

A rate in criminal justice is how often something happens per 100,000 people. (Rates don't have to be per 100,000, but in criminal justice statistics, they almost always are.)

If Baltimore had 300 homicides and a population of 1,000,000 people (in reality both numbers are smaller, but I want to keep the math easy), the rate tells us how many homicides there are per 100,000 people. 100,000 is one-tenth of one million. So the homicide rate will be one-tenth the homicide number. You should be able to do that in your head, but on a calculator, divide 100,000 by 1,000,000. You get 0.1. So to convert Baltimore's homicide numbers to a homicide rate, you multiply the homicide numbers by 0.1 (the same as dividing by 10). Baltimore's homicide rate (per 100,000) would be 30.

New York City is larger. Much larger. About eight million people. In figuring out the homicide rate, we're asking a hypothetical question about how many homicides New York would have if it had a population of 100,000. Then we can compare it Baltimore's rate.

To do this in your head, if the numbers are nice are round, figure how many times 100,000 goes into the population 8,000,000. The answer is 80. And since we're saying New York has 400 homicides a year, we would divide the number of homicides 400 by 80, which gives us a homicide rate of 5.

Same thing a different way, on your calculator. Take 100,000 and divide by 8,000,000. This gives you 0.0125. Multiply 0.0125 by the number of homicides, 400. This gives you a homicide rate or 5.

New York City has a homicide rate of 5; Baltimore's homicide rate is 30, or 6 times higher than New York's, even though New York has more murders.

And here's one way to check your work. The rate is per 100,000. So if the population is less than 100,000, the rate will be greater than the number (a town with 50,000 people and 2 homicides has a homicide rate of 4 per 100,000). If the population is greater than 100,000, the rate will be less than the number (a town of 200,000 people has 8 homicides, the homicide rate is 4 per 100,000).