University Of Maryland University College STAT200 Assignment

University of Maryland University College STAT200 - Assignment #2: Descriptive Statistics Analysis and Writeup

From the dataset, I chose UniqueID# 36. I am married with an annual income of $99,610. I am the head of the household and I am 36. It is only two of us, me and my spouse. We both have our bachelor’s degrees and are both employed. Our annual income is a total of both our incomes together in the household.

Variables Selected for the Analysis

Data Set Description and Method Used for Analysis

The data is undertaken by making random sampling from the US department of labor’s 2016 consumer expenditure surveys. The data includes the annual expenditures of 30 households. For the analysis, we are using four socioeconomic variables and four expenditure variables. Here we have undertaken the annual household income in USD, head of the household’s age group, household family size, the total amount of expenditure of food annually, and the total amount of expenditure on entertainment annually as the variables.

Results

Variable 1: Income Numerical Summary

Graph: Histogram of Income

Analysis of the annual household income shows a mean of approximately $99,661, with a median slightly lower at $97,305, indicating a relatively symmetric distribution with some outliers on the higher end. The histogram illustrates that most households' income falls around the mid-90,000s to 110,000 USD range, with a distribution that appears approximately normal but slightly skewed.

The median income in this data set is higher than the national median reported by the 2017 U.S. Census Bureau, which was $59,039, indicating that this sample represents households with higher-than-average income levels. The standard deviation suggests moderate variability in household incomes within this sample.

Variable 2: Age Head of Household Numerical Summary

Graph: Box plot of Age Distribution

The average age of the household head is approximately 47 years, with a median of 50 years, indicating a relatively symmetric age distribution, slightly skewed toward older ages. The standard deviation of 8.48 years suggests most household heads fall within the age range of 39 to 55 years. The box plot visually demonstrates the spread and potential outliers in age data.

This age profile aligns with typical working-age adults who are establishing or maintaining household finances, consistent with the sampled household's higher income levels.

Variable 3: Family Size Numerical Summary

Graph: Pie chart of Family Size

The average family size is approximately 2.83 members per household, with a standard deviation of 1.02 indicating most families consist of 2 to 4 members. The pie chart shows that the majority of households fall into the small to medium family categories, with most family sizes being 2, 3, or 4 members.

This aligns with expectations for higher-income households, often composed of young couples or small families.

Variable 4: Annual Food Expenditure Numerical Summary

Graph: Histogram of Food Expenditure

The average annual expenditure on food is approximately $8,505, with variability indicated by a standard deviation of $1,646.07. The histogram shows a relatively normal distribution centered around this mean, with some variation but no extreme outliers. This expenditure aligns with typical household food budgets considering higher income levels.

Variable 5: Annual Entertainment Expenditure Numerical Summary

Graph: Histogram of Entertainment Expenditure

The mean annual expenditure on entertainment is roughly $111, with a standard deviation of $38.21, suggesting moderate variation among households. The histogram indicates a distribution skewed slightly toward lower expenditures but generally centered around the mean, typical for households with higher income levels.

Discussion and Conclusion

Overall, the analysis indicates that the sampled households tend to have higher-than-average incomes relative to national data, with household income averaging nearly $100,000. The household heads are typically mid-40s, which aligns with active working-age adults. Family sizes are generally small, averaging less than three members, consistent with higher-income brackets where smaller families are common. Expenditures on food are substantial, around $8,505 annually, which is proportional to the household income, suggesting a comfortable standard of living. Entertainment expenditures, averaging around $111 annually, reflect discretionary spending typical of higher-income households.

The histograms and box plots support the conclusion that most variables—income, age, expenses—are approximately normally distributed, with some slight skewness in age and expenditures. The data's distribution patterns offer valuable insights into household behavior and spending patterns at higher income levels. These insights could assist in household budget planning, highlighting areas for discretionary spending or savings.

References

• Bureau of Labor Statistics. (2017). Consumer Expenditure Surveys. U.S. Department of Labor. https://www.bls.gov/cex
• Kozak, M. (2020). Statistical Inference: Confidence intervals and hypothesis testing. Journal of Statistical Methods.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
• Hill, R., & Lewicki, P. (2006). Statistics: Methods and Applications. StatSoft.
• Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data. Pearson.
• Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press.
• Laerd Statistics. (2018). Descriptive statistics. https://statistics.laerd.com/statistical-guides/descriptive-statistics.php
• Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
• McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.