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The table gives the prison population and total population for a sample of states in \(2014-15 .\) (Source: The 2017 World Almanac and Book of Facts) \begin{tabular}{|l|c|c|} \hline State & Prison Population & Total Population \\ \hline California & 136,088 & \(39,144,818\) \\ \hline New York & 52,518 & \(19,795,791\) \\ \hline Illinois & 48,278 & \(12,859,995\) \\ \hline Louisiana & 38,030 & \(4,670,724\) \\ \hline Mississippi & 18,793 & \(2,992,333\) \\ \hline \end{tabular} Find the number of people in prison per thousand residents in each state and rank each state from the highest rate (rank 1) to the lowest rank (rank 6). Compare these rankings of rates with the ranks of total numbers of people in prison. Of the states in this table, which state has the highest prison population? Which state has the highest rate of imprisonment? Explain why these two answers are different.

Step by step solution

01

Calculate Rates for Each State

First, calculate the rate of imprisonment for each state. This is done by dividing the prison population by the total population and then multiplying by 1000 to get the rate per thousand. This will give the numbers: \[\frac{136088}{39144818} * 1000 = 3.48\] \[\frac{52518}{19795791} * 1000 = 2.65\] \[\frac{48278}{12859995} * 1000 = 3.75\] \[\frac{38030}{4670724} * 1000 = 8.14\] \[\frac{18793}{2992333} * 1000 = 6.29\].

02

Rank the States

Now, rank each state from the highest rate (rank 1) to the lowest rank (rank 6). The numbers calculated above will translate to the following rankings: 1. Louisiana, 2. Mississippi, 3. Illinois, 4. California, 5. New York.

03

Compare Rankings

Next, compare these rank rates with the ranks of total numbers of people in prison. The rankings of total numbers of people in prison are: 1. California, 2. New York, 3. Illinois, 4. Louisiana, 5. Mississippi. Even though California has the highest overall prison population, it has a lower rate of imprisonment than Louisiana or Mississippi because its total population is much larger. Similarly, even though New York has the second highest overall prison population, it has the lowest rate of imprisonment because its total population is also considerably larger than the other states. This demonstrates that the rate of imprisonment and total prison population can show different trends.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Imprisonment Rate

Understanding the imprisonment rate is crucial when analyzing crime and punishment trends within a state. The imprisonment rate is calculated by determining the number of prisoners per 1,000 residents. To find this rate:

• Divide the prison population by the total population
• Multiply the result by 1,000

This method allows for a straightforward comparison between states, regardless of their overall populations. For example, even though California has an extensive prison population, its imprisonment rate is lower due to its large total population. This calculation provides a clearer picture of the actual density of prisoners relative to the population size.

Population Statistics

Population statistics play a significant role in understanding various socio-economic factors, including imprisonment rates. These statistics include both the total population of a state and subcategories such as prison populations. Analyzing these numbers gives insights into the demographics of a state, such as:

• The total population's size
• The proportion that makes up the prison population

A small prison population in a state with a small total population might result in a high imprisonment rate, demonstrating how relative comparisons are essential. For instance, Louisiana's high imprisonment rate results from its smaller total population, even with a smaller prison population than California. Without these statistics, understanding the context of imprisonment rates across various states would be challenging.

Ranking Methodology

The ranking methodology is a method used to order or sequence items based on specific criteria, such as rates or totals. In analyzing prison data, states can be ranked by total prison populations or by imprisonment rates. When ranking by imprisonment rates:

• Calculate the rate as described above, using the formula
• Order from highest to lowest rate

On the other hand, ranking by the total number of prisoners involves a straightforward ordering from the most to the least. The methodology used depends on what aspect of the data analysis is most valuable or revealing. This approach is vital for policy comparisons and understanding crime and punishment trends.

State Comparisons

State comparisons regarding imprisonment highlight the differences in criminal justice policies and socio-economic factors between regions. By comparing imprisonment rates rather than just total populations, one can see which states have a more significant proportion of their population in prison. For example:

• Louisiana, with a small overall population but relatively high prison population, shows a higher imprisonment rate than larger states like California.
• New York, despite having a substantial number of prisoners, shows the lowest imprisonment rate due to its large general population.

Such comparisons allow for critical analysis of each state's approach to law enforcement and the effectiveness of its criminal justice system. Furthermore, they can guide policy development to address current incarceration trends in relation to population size.