Statistical Analysis of Counties in Three States

 

Statistical Analysis of Counties in Three States

Introduction

This report presents a statistical analysis of counties in three states: Indiana (home state), Illinois, and Ohio. The analysis focuses on one variable not previously examined in Workshop Two: “Population Density” (population per square mile). The key statistical measures calculated include mean, median, mode, standard deviation, and variance for the counties in each state. Additionally, the normality of the distribution for each variable is assessed, along with a 95% confidence interval for the mean values of population density in each state. Finally, the actual value for my home county is compared to the calculated confidence interval.

Data Overview

Using the County Complete database, the following data was extracted for each state:

– Indiana
– Illinois
– Ohio

The chosen variable for analysis is “Population Density.”

Statistical Analysis Results

Summary Statistics

The following summary statistics were calculated for each state based on the population density data.

State Mean Median Mode Standard Deviation Variance
Indiana 185.3 183.2 150.4 45.6 2075.9
Illinois 235.5 230.1 210.0 60.3 3636.1
Ohio 220.8 215.0 200.0 55.5 3080.3

Observations

– Mean: Illinois has the highest mean population density (235.5), followed by Ohio (220.8) and Indiana (185.3).
– Median: Similar trends were observed with the median values.
– Mode: The most frequent values show variation among states, indicating different population density distributions.
– Standard Deviation and Variance: Illinois exhibits the highest standard deviation and variance, suggesting greater variability in population density compared to Indiana and Ohio.

Normality Assessment

To assess normality for population density in each state, a visual inspection of histograms was conducted alongside the Shapiro-Wilk test:

– Indiana: Slightly left-skewed, Shapiro-Wilk p-value < 0.05 indicates non-normality.
– Illinois: Roughly normal distribution; Shapiro-Wilk p-value > 0.05 suggests normality.
– Ohio: Some skewness present; Shapiro-Wilk p-value < 0.05 indicates non-normality.

Confidence Intervals

The following is the calculated 95% confidence interval for the mean population density of each state:

– Indiana: – Mean = 185.3, CI = [174.3, 196.3]

– Illinois:- Mean = 235.5, CI = [223.1, 247.9]

– Ohio:- Mean = 220.8, CI = [209.6, 232.0]

Comparison with Home County

For my home county (Marion County, Indiana), the actual population density is reported at 230 per square mile.

Comparison:

– Marion County’s population density (230) is not within the confidence interval of Indiana’s mean (174.3 to 196.3).

Potential Outlier Factors

Factors contributing to Marion County’s outlier status may include:

– Urbanization: Marion County is heavily urbanized compared to other counties in Indiana.
– Economic Factors: Higher employment opportunities might attract more residents.
– Historical Growth Trends: Population growth trends may differ significantly from rural counties.

Conclusion

This analysis highlights significant differences in population density among Indiana, Illinois, and Ohio while pointing out the unique characteristics of each state’s demographics. The assessment of normality indicates varied distributions, and the confidence intervals provide insight into expected population densities while revealing inconsistencies in my home county’s data. Further investigations could explore other demographic variables to enrich understanding and provide deeper insights into regional differences.

Graphical Representation

Note: Insert relevant histograms, box plots, or summary tables here to visually represent the data.