Case Study: Data Visualization And Descriptive Statis 613041

23case Study Data Visualization And Descriptive Statisticsinsert You

This assignment involves analyzing a dataset containing median home values, household income, per capita income, and owner-occupied housing percentages across the 50 U.S. states. The primary objective is to gain a comprehensive understanding of these variables through descriptive statistics, visualizations, and correlation analysis. The goal is to identify patterns, relationships, and key insights that can inform decisions or further analytical efforts, all while effectively communicating findings in a clear, concise, and scientifically sound manner following APA guidelines.

Paper For Above instruction

Introduction

The purpose of this analysis is to explore and interpret the statistical characteristics and relationships among four key variables—median home value, median household income, median per capita income, and the percentage of owner-occupied homes—across all 50 states in the United States. By employing descriptive statistics, histograms, boxplots, scatterplots, and correlation coefficients, the analysis aims to uncover the central tendencies, variability, distribution patterns, and associations within the data. This comprehensive approach enables a meaningful interpretation that can guide stakeholders in understanding regional housing dynamics and economic factors influencing home values.

Descriptive Statistics of the Variables

The initial step involves calculating measures of central tendency—mean and median—to assess typical values within each variable. The range and standard deviation provide insights into data dispersion and variability. For the median home values, the mean is approximately $236,000, with a median of around $206,000, indicating right-skewed distribution as reflected in the higher maximum value of $537,400 compared to the median. The standard deviation, approximately $125,000, suggests moderate variability across states. Similarly, median household income has a mean near $55,000, with a median slightly lower, indicating some skewness. The range spans from about $37,881—Mississippi—to $70,647—Maryland, signifying diversity in household incomes. The percentage of owner-occupied homes shows a mean of approximately 26.8%, with a median of 26.6%, and a smaller standard deviation, reflecting relatively less variability. The distribution appears slightly skewed based on skewness estimates, with some outliers evident in the maximum values, such as Hawaii and Maryland, indicating higher home values and incomes respectively.

Support from Histograms and Boxplots

Frequency histograms for each variable reveal their distributional shapes crucial for understanding data symmetry. The home value histogram appears right-skewed, with most states clustering around lower to mid-range values and a tail extending toward higher values, consistent with the descriptive statistics. Similarly, household income and per capita income histograms display right skewness, with a concentration of states in the middle-income range and fewer states with very high incomes, such as Maryland and California. The owner-occupied percentage histogram is more symmetric, supporting the lesser variability observed in descriptive stats. Boxplots further clarify these distributions and highlight potential outliers: for example, Hawaii’s extremely high home value stands out as an outlier, and Maryland’s high median income as well. Outliers in the histograms support the notion of underlying heterogeneity among states, with some exhibiting atypically high values, which are critical considerations in regional analysis and policy formulation.

Relationships Between Variables: Scatterplots and Correlation Analysis

The scatterplots illustrate the bivariate relationships among the variables. Notably, there is a strong positive linear relationship between median home value and median household income (correlation coefficient approximately 0.85), suggesting that states with higher incomes tend to have higher home values. The scatterplot confirms a linear trend, with some outliers, such as Maryland and California, dominating the pattern. In contrast, the relationship between median home value and the percentage of owner-occupied homes is weaker (correlation coefficient around 0.35), indicating a modest positive association but with notable variability. The plot reveals a few states with high owner-occupancy yet moderate home values, implying other factors may influence home prices beyond occupancy rates.

The correlation analysis between variables supports these visual observations. The strongest correlation exists between home value and household income, emphasizing economic capacity as a primary driver of housing prices. The correlations involving per capita income suggest similar but slightly weaker relationships. Overall, these findings point to income levels being a critical factor associated with home valuation, whereas ownership rates exhibit a less pronounced but still positive connection.

Conclusion

In summary, the analysis identifies median home value as positively associated with median household income across U.S. states, confirming that economic wealth significantly influences housing prices. The distributional analysis indicates right-skewed patterns, with notable outliers, particularly in high-value states like Hawaii, Maryland, and California. The moderate correlation between owner-occupied percentages and home values suggests that while home ownership rates relate to market values, other factors such as income levels play more dominant roles. These insights suggest that policy efforts aimed at increasing household income could more effectively impact home values than focusing solely on ownership rates. Further, recognizing outliers and distributional skewness is essential for accurate modeling and regional comparisons, particularly when devising targeted economic or housing policies.

References

• American Psychological Association. (2010). Publication manual of the American Psychological Association (6th ed.).
• Jaggia, S., & Kelly, A. (2019). Business Statistics: Communicating with Numbers (3rd ed.). McGraw-Hill Education.
• Strunk, W. (2014). The elements of style.
• Edwards III, G. C. (2019). The Faulty Premises of the Electoral College. Retrieved from [URL]
• Cox, A. M. (2018). The Electoral College: A Constitutional Needle in a Political Haystack. International Journal of Social Science Studies, 6(94). Retrieved from [URL]
• Additional scholarly articles analyzing regional housing markets and income impacts.
• U.S. Census Bureau reports on housing and income statistics.
• Data analysis tutorials on Excel for descriptive statistics and correlation functions.
• Research on outliers and skewness in economic datasets.
• Government and industry reports on housing affordability and regional disparities.