Question

The town of Shinbone, Kansas, has a population of 211,732 and experienced 47 bank robberies, 13 murders, and 23 auto thefts during the past year. Compute a rate for each type of crime per 100,000 population. (HINT: Make sure that you set up the fraction with size of population in the denominator:)

Short answer

Bank Robberies: 22.19, Murders: 6.14, Auto Thefts: 10.86 per 100,000 people.

Step-by-step solution

- Set Up the Fractions

For each type of crime, create a fraction with the number of crimes as the numerator and the total population (211,732) as the denominator.

- Bank Robberies

The fraction for bank robberies is \(\frac{47}{211732}\).

- Convert to Rate Per 100,000

To convert it to a rate per 100,000 population, multiply by 100,000: \[ \left(\frac{47}{211732}\right) * 100000 \approx 22.19 \]

- Murders

The fraction for murders is \(\frac{13}{211732}\).

- Convert to Rate Per 100,000

Multiply by 100,000: \[ \left(\frac{13}{211732}\right) * 100000 \approx 6.14 \]

- Auto Thefts

The fraction for auto thefts is \(\frac{23}{211732}\).

- Convert to Rate Per 100,000

Multiply by 100,000: \[ \left(\frac{23}{211732}\right) * 100000 \approx 10.86 \]

Key concepts

Population

Population is the total number of people living in a specific area. This could be a town, city, or even an entire country. Understanding the population helps in many fields, like economics, urban planning, and public health.
In our exercise, Shinbone, Kansas, has a population of 211,732. This large number is used to find crime rates.
Why do we need the population number for crime rate calculations? Because it sets a base for understanding how widespread the crime is. If you only have the number of crimes but not the number of people, it’s hard to tell how significant the problem is.
Simply put, more people usually mean more total crime, but the rate at which crime occurs (per 100,000 people) can help us compare different areas fairly.

Crime Statistics

Crime statistics are data that show the number of crimes that have occurred. These stats can include various types of crimes, like bank robberies, murders, and auto thefts, as in our example.
Having accurate crime statistics helps authorities understand the safety of an area. It also aids in law enforcement and crime prevention.
For Shinbone, Kansas, we have:

• 47 bank robberies
• 13 murders
• 23 auto thefts

Each of these figures tells us how many incidents happened but doesn't yet give us a fair measure to compare with different sized towns. This is why we need to calculate the crime rate per 100,000 population.

Rate Per 100,000

The rate per 100,000 people offers a standardized way to measure and compare crime across different populations.
Why use 100,000? It's a convenient number that makes it easier to understand frequency and probability.
To find this rate, follow these steps:

• Create a fraction with the number of crimes as the numerator and the population as the denominator. For example, for bank robberies in Shinbone, we create \(\frac{47}{211732}\).
• Multiply this fraction by 100,000 to scale it appropriately.

For example: \[ \left( \frac{47}{211732} \right) * 100000 \approx 22.19 \]Use this method for other crimes:

• Murder: \[ \left( \frac{13}{211732} \right) * 100000 \approx 6.14 \]
• Auto theft: \[ \left( \frac{23}{211732} \right) * 100000 \approx 10.86 \]

This tells us, on average, how often each crime occurs per 100,000 people, making it easier to spot trends and make data-informed decisions.