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Give an example explaining how politicians on both sides of an issue can use numbers to support their case without lying.

Suppose a candidate is running for mayor of a city. During the incumbent mayor's first year in office, the city had a population of 25,000, and 50 violent crimes were committed. During the incumbent mayor's most recent year in office, the city had a population of 30,000, and 55 violent crimes were committed.

1. One side might argue that the number of crimes has increased, with 55 violent crimes having been committed during the incumbent mayor's most recent year in office compared to 50 crimes during the first year in office.

2. The other side might argue that the crime rate has decreased, with a rate of 1 violent crime for every 500 people during the incumbent mayor's first year in office and a rate of 1 violent crime for every 545 people during the incumbent mayor's most recent year in office.

(Round to the nearest whole number as needed.)

Answer :

Sure! Let's analyze the situation step-by-step.

We have two sets of data relating to violent crimes in a city during two different periods: the incumbent mayor's first year in office and the most recent year in office.

1. Initial Data:
- First Year:
- Population: 25,000 people
- Violent Crimes: 50 crimes

- Most Recent Year:
- Population: 30,000 people
- Violent Crimes: 55 crimes

2. Calculation of Crime Increase:
- The number of violent crimes increased from 50 to 55.
- This is an increase of [tex]\( 55 - 50 = 5 \)[/tex] violent crimes.

3. Crime Rate Calculations:
- First Year Crime Rate:
- Crime rate is the population divided by the number of violent crimes.
- For the first year: [tex]\( \frac{25,000}{50} = 500 \)[/tex]
- This implies there was 1 violent crime for every 500 people.

- Most Recent Year Crime Rate:
- For the recent year: [tex]\( \frac{30,000}{55} \approx 545 \)[/tex] (rounded to the nearest whole number)
- This implies there was 1 violent crime for about every 545 people.

4. Interpreting the Data:
- A politician arguing that crime is increasing might focus on the increase in the number of crimes, which went up by 5.
- A politician arguing that the city is becoming safer might focus on the crime rate, which decreased. The crime rate went from 1 crime per 500 people in the first year to about 1 crime per 545 people in the most recent year.

This example shows that both sides can use numbers to support their viewpoints without lying, by emphasizing different aspects of the data – total number of crimes vs. crime rate.

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