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Given the provided information, the core assignment is to analyze various statistical and financial problems including percentage calculations, data analysis (mean, median, mode, standard deviation), frequency distribution, and interpretation of data related to budgets, grades, employee leaves, and hourly wages. The associated tasks include calculating percentages, finding measures of central tendency and variability, constructing frequency tables, and analyzing data to produce insights for decision-making.

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This paper comprehensively addresses real-world data analysis problems relevant to finance, education, and workforce management. The tasks presented involve multiple statistical calculations and data interpretation methods essential for informed decision-making and strategic planning.

First, the problem of computing the percentage of sales over a specific period relative to the yearly sales requires understanding of basic percentage calculation. If sales for October to December are part of an annual total, then dividing these quarterly sales figures by the total yearly sales, and then multiplying by 100, yields the percentage. Assuming hypothetical sales data—if the sales from October to December added up to a certain amount, say $X, then the formula is:

Percentage = (Sales from October to December / Total yearly sales) × 100

This measure helps in understanding seasonal or quarterly variations within a fiscal year, which influence strategic marketing and resource allocation.

Secondly, analyzing a family budget involves percentage calculations for expenditure on education. Summing expenses categorized under education, savings, and miscellaneous—such as Education ($144), Savings ($170), and Miscellaneous ($70)—total $384. If the family's take-home pay is, for example, $1,200, then the percentage spent on education is:

Percent for education = (Expenses for education / Total take-home pay) × 100 = (144 / 1200) × 100 ≈ 12%

This insight helps assess budgeting priorities and financial planning effectiveness.

Next, weekly expenses of students are analyzed to compute measures of central tendency: mean, median, and mode. For a set of data such as [e.g., 15, 20, 15, 25, 20], the mean is calculated as the sum divided by number of observations, the median as the middle value after sorting, and the mode as the most frequent value. These measures are essential to understanding typical expenses and identifying outliers or patterns within the data.

In the case of grades, determining the percentage of students scoring below 80 involves counting entries below this threshold, dividing by total number of students, and multiplying by 100. For example, if out of 50 students, 20 scored below 80, then the percentage is (20/50) × 100 = 40%.

Standard deviation calculations for series like ACT scores—e.g., 28, 26, 16, 14—measure variability within the data. Computing the standard deviation involves finding deviations from the mean, squaring these deviations, summing them, dividing by the number of data points minus one (for sample standard deviation), and taking the square root. This reflects the spread of test scores, indicating consistency or variability among test-takers.

Regarding employee medical leave days, calculating the sum of squares involves computing deviations from the mean, squaring these deviations, and summing them. For data points like 18, 12, 21, 15, 24, 18, the mean can be calculated, followed by deviations, squares, and summation. This statistic is useful in variance and standard deviation computations, indicating variability in employee leave durations due to on-the-job accidents.

The frequency distribution based on hourly wages, such as $15, $18, $6, etc., is built by classifying wages into class intervals, counting the number of wages within each interval, and computing midpoints. This facilitates analysis of wage distributions, helping institutions understand wage gaps and labor market conditions.

Median salary calculations involve organizing salary data in order and selecting the middle value(s). In case of even numbers, it is the average of two middle values. This measure provides an understanding of the typical salary level, less affected by outliers than the mean.

Overall, these data-driven tasks demonstrate core statistical skills in analysis, interpretation, and visualization of real-world data, enabling better decision-making in business, education, and human resources. These statistics inform strategies related to financial planning, resource allocation, employee management, and policy formulation.

References

  • Foster, D. (2020). Business Statistics: Communicating with Numbers. McGraw-Hill Education.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics (8th ed.). Pearson.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W.H. Freeman.
  • Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis (7th ed.). Cengage Learning.
  • Ryan, T. P. (2013). Modern Business Statistics with Microsoft Excel. Pearson.
  • American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.).
  • U.S. Bureau of Labor Statistics. (2023). Occupational Employment and Wages. U.S. Department of Labor.
  • U.S. Census Bureau. (2022). Demographic and Economic Data. U.S. Government.
  • National Center for Education Statistics. (2021). Data on Education Expenditure and Student Performance. U.S. Department of Education.
  • OECD. (2022). Education at a Glance. Organisation for Economic Co-operation and Development.

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