Descriptive Statistics Analysis and Writeup

  Introduction: A married male is aged 50 and a head of household in a family of four (father, mother and two children). He is an accountant earning an average of $110,000. $90,000 is spent in household expenses. On average, $11,000 is spent in food, $30,000 on housing and $70 spent on transport for fuel and vehicle service costs. He would like to determine the average income levels of Americans within his age bracket and the average expenditure of other Americans within the same income group. The analysis intends to find whether there exists any statistically significant difference between the given income and expenditure levels from the general population’s levels. The analysis is relevant to enable decision making on adjusting the spending habit. Table 1. Variables Selected for the Analysis Variable Name in data set Description Type of Variable (Qualitative or Quantitative) Variable 1: “Income” Annual household income in USD. Quantitative Variable 2: “Age” Age of the Head of Household Quantitative Variable 3: “Marital status” Marital Status of Head of Household Qualitative Variable 4: “Family size” Total Number of People in Family (Both Adults and Children) Quantitative Variable 5: “Annual expenditure Total Amount of Annual Expenditures Quantitative Data Set Description and Method Used for Analysis: The analysis used a dataset of a sample of 31 US households’ data of their annual incomes and expenditure levels. The dataset is a random sample from the US Department of Labor’s 2016 Consumer Expenditure Surveys (CE). Given the dataset of a sample of Americans’ details, the data was analyzed descriptively using the measures of central tendency and measures of dispersion. The descriptive analysis was done in MS Excel. The analysis determined the mean, median and standard deviation of income and annual expenditure; mean median and range of ages, mode of marital status and mean and standard deviation of family sizes. The variables are further presented in form of graphs and charts. Results: Variable 1: Income Numerical Summary Table 2. Descriptive Analysis for Variable 1 Variable n Measure(s) of Central Tendency Measure(s) of Dispersion Variable: Income 31 Median= 97681 SD = 5775.58 Graph and/or Table: Histogram of Income Description of Findings The variable was selected to determine the average income levels of the population within the dataset for comparison with the case income level. It was found that Americans earn an average of $100,539, with an individual household’s income earning deviating by $5775.58 from the mean. The medium income earned is $97,681, being the income level earned by about half of the population. In the case, the individual earning $110,000 has a higher income than the average earned by Americans. The majority of Americans (58% being 18 out of 31) earn about $98,000 as presented in the histogram. Notably, about 25% of the population earn at least $110,000 per year. Variable 2: Age Numerical Summary Table 3. Descriptive Analysis for Variable 2 Variable n Measure(s) of Central Tendency Measure(s) of Dispersion Variable: Age 31 Mean = 48.52 Range = 36 Graph and/or Table: Bar graph of age Description of Findings The analysis aimed at establishing the average age of American citizens for comparison with the case individual’s age. It was found that the population has an average of 48.52 years and a 36 year range between the youngest (31 years) and the oldest (67 years). In the case, the individual’s age of 50 is slightly above the mean. The findings revealed that the largest cohort of the population (37.5%) is aged between 51 and 60 years while the least cohort (6%) is of individuals aged 66 to 70. Variable 3: Marital status Numerical Summary. Table 4. Descriptive Analysis for Variable 3 Variable n Measure(s) of Central Tendency Measure(s) of Dispersion Variable: Marital status 31 N/A Mode = Married Graph and/or Table: Pie chart of marital status Description of Findings The analysis for the variable sought to assess the expenditure differences between married and unmarried. It was found that most of the populations (58%) are married while 48% are not married. Variable 4: Family size Numerical Summary Table 5. Descriptive Analysis for Variable 4 Variable n Measure(s) of Central Tendency Measure(s) of Dispersion Variable 4: Family size 31 Mean = 3.35 SD = 1.28 Graph and/or Table: Column chart of family sizes Description of Findings The family size affects the actual expenditure incurred by the household head on the household’s annual expenditure. The analysis of the variable sought to assess the differences in expenditure among varying family sizes. It was found that the households in the population have a mean family size of 3.35 (about 4 people). Similarly, majority of the households within the population (39%) have family sizes of 4 (summarized in the chart) while the least (3.2%) have 6 family members. The number of family members varies by 1.28. Variable 5: Annual expenditure Numerical Summary   Table 6. Descriptive Analysis for Variable 5 Variable n Measure(s) of Central Tendency Measure(s) of Dispersion Variable: Annual expenditure 31 Mean = 67245 SD = 12119 Graph and/or Table: Histogram of annual expenditure Description of Findings It was found that the American population incurs an average expenditure of $67,245 per annum, with a deviation of $12,119 from the mean expenditure. Majority of the population (48%) spends around $60,000, which is slightly less than the population’s average expenditure. The variable analysis aimed at determining the average expenditure incurred by the US households for comparison with my household’s expenditure. In the case household with an annual expenditure of $90,000, it is evident that the household expenditure is far above the population mean (in excess with 50% over the population mean expenditure). The high expenditure requires investigation into expenditure drivers to devise means of minimizing household expenses. Discussion and Conclusion The summary of the main findings is presented in table 7 below.   Table 7: Summary of the findings Row Labels Average of Income Average of Age Average of Annual Expenditure Average of Family size Married 104,012 47.81 77,836 3.88 Not Married 96,834 49.27 55,948 2.80 Grand Total 100,539 48.52 67,245 3.35 Case Household: Married 110,000 50 90,000 4 The main aim of the descriptive analysis was to determine the income and expenditure statistics of the sample population for comparison against the case household income and expenditure to guide decision making on expenditure habits. It was found that the population earns an average income of $100,539, out of which $67,245 is averagely spent on household expenditure. The population has an average age of 48.52 years, 52% of whom are married and 48% unmarried. Majority of the unmarried individuals are older, with an average of 49.27 years than the married who average 47.81 years. The population has an average family size of 3.34. The analysis summarized in table 7 presents that married individuals earn higher income, with an average of $104,012 than the unmarried household heads who earn averagely $96,834. Accordingly, married household heads incur higher annual expenditure of $77,836 on average than the unmarried who incurs $55,948. The higher annual expenditure levels are attributed to increased family sizes, where married household heads have an average of 3.88 members while unmarried heads have 2.8. In the case household, the annual income earned ($110,000) exceeds the populations average. Therefore, it is evidently concluded that the household head is among the high-income earners within the population. He earns an income exceeding other married men, and consequently spends excessively higher than other household heads within similar social characteristics. Notably, while the population of married individuals with about 4 household members spends about $77,836 annually, he spends $90,000, 15.6% higher than the expected average. Thus, is evident that the individual has reasonably poor spending habit which requires control. To enable expenditure control decisions and identify the excessively expended areas, further analysis of additional variables on expenditure items is necessary, including amount spent on food, transport and housing, which were not analyzed in this study.       • Develop a plan to calculate inferential statistics on a set of real world data (reference sources) • Conduct the analysis • Write up results.