In our comprehensive study, we meticulously investigate the distribution of homicide rates per 100,000 residents. Through quartile-based population grouping, we reveal intriguing patterns in cities of varying sizes. Our analysis, which includes detailed tables for each group, provides valuable insights into how homicide rates fluctuate in correlation with population. This study offers a profound understanding of the dynamics of crime in diverse urban settings, shedding light on the challenges and opportunities for crime prevention.

## Assignment: Analyzing Homicide Rates in New York State Cities

## Problem Description:

In this statistics analysis assignment, we delve into the distribution of homicide rates per 100,000 inhabitants across various cities in New York State. Our objective is to explore how these rates are distributed across different population groups and analyze the statistical characteristics of each group.

## Solution

## Report:

**Table 1: Quartiles of the Population of New York State Cities**

To initiate our analysis, we first divided the dataset into four population groups using quartiles. The quartiles for the population of New York State cities are as follows:

Quartiles | Population |

Q1 | 2,765 |

Q2 | 6,595 |

Q3 | 17,470 |

This table shows that:

- 25% of the cities have populations less than or equal to 2,765 people.
- 50% of the cities have populations less than or equal to 6,595 people.
- 75% of the cities have populations less than or equal to 17,470 people.

**Table 2: Distribution of Groups**

We then categorized the cities into four groups based on these quartiles:

Group | Population |

1 | <=2,765 |

2 | 2,766 to 6,595 |

3 | 6,596 to 17,470 |

4 | >=17,471 |

Now, let's analyze the homicide rates for each group:

**Descriptive Statistics of Rate of Murder per 100k for Group 1**

**Group 1: Cities with Population <= 2,765**

- The mean rate of murder per 100,000 is 0.
- The standard error is 0.
- The median, mode, and standard deviation are also 0.
- There is no variance, kurtosis, or skewness, indicating that the rates are constant.

**Descriptive Statistics of Rate of Murder per 100k for Group 2**

**Group 2: Cities with Population 2,766 to 6,595**

- The mean rate of murder per 100,000 is 0.68.
- The standard error is 0.39.
- The median is 0.00, indicating that 50% of the cities have a rate of 0.00.
- The most frequent rate is 0.00.
- The standard deviation is 3.85, suggesting some variation.
- The skewness coefficient is 5.69, indicating a right-skewed distribution.

**Descriptive Statistics of Rate of Murder per 100k for Group 3**

**Group 3: Cities with Population 6,596 to 17,470**

- The mean rate of murder per 100,000 is 1.11.
- The standard error is 0.33.
- The median is 0.00, indicating that 50% of the cities have a rate of 0.00.
- The most frequent rate is 0.00.
- The standard deviation is 3.22, suggesting some variation.
- The skewness coefficient is 2.88, indicating a right-skewed distribution.

**Descriptive Statistics of Rate of Murder per 100k for Group 4**

**Group 4: Cities with Population >= 17,471**

- The mean rate of murder per 100,000 is 2.59.
- The standard error is 0.46.
- The median is 0.00, indicating that 50% of the cities have a rate of 0.00.
- The most frequent rate is 0.00.
- The standard deviation is 4.47, suggesting some variation.
- The skewness coefficient is 2.58, indicating a right-skewed distribution.

## Discussion:

For Group 1, the homicide rate per 100,000 is a constant value of zero, leading to zero dispersion measures. Skewness and kurtosis coefficients are undefined due to the constant values.

In Group 2, most cities have a murder rate of zero, with only three cities showing rates different from zero, ranging from 18.09 to 26.44.

In Group 3, eleven cities have non-zero rates, ranging from 6.32 to 15.00.

In Group 4, forty cities have non-zero rates, ranging from 1.29 to 24.19.

This analysis provides insights into how homicide rates vary across different population groups within New York State cities, showing distinct patterns and variations in the data.

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