Spring 2015 Math 130 Midterm Exam On Independent States

Spring 2015 Math 130 Midterm Exami N D E P E N D E N T S T U D Y

Collect the ages (in years) of all your family members (parents, siblings) and extended family members (grandparents, aunts, uncles, cousins). Collect no more than 20 ages. Create a table with each individual's name, relation to you, and age. Make a stem-and-leaf plot displaying all ages, and a back-to-back stem-and-leaf plot for males and females. Construct a histogram showing the number of individuals in specified age groups: babies (0-1), children (2-12), teens, young adults (20-29), adults, seniors (70+). Calculate and present the mean, median, mode, variance, and standard deviation for all data, as well as for males and females separately. Find quartiles and draw box-and-whisker plots for each group. Using collected data, answer probability and counting questions involving the selection of family members from different categories, and other scenarios like family ride arrangements and market sizes. Present all calculations clearly, organize your work on separate pages, and follow the specified order. Include a title page with your name, and staple all pages together. Your grade depends on the completeness, accuracy, neatness, and organization of your work. The project is due on Monday, May 11th, 2015, at 1:00 pm.

Paper For Above instruction

This project serves as a comprehensive application of fundamental statistical and probabilistic concepts through the analysis of personal familial data. It emphasizes the importance of data collection, visualization, descriptive statistics, and probability calculations in understanding real-world data contexts.

Beginning with data collection, the student gathers ages of family members, including relatives of various relations. The process promotes thoughtful data organization, combining qualitative information (relation and name) with quantitative age data. This foundational step enhances understanding of categorizing and tabulating data systematically. The created tables serve as the basis for subsequent graphical and statistical analysis.

The construction of different graphical representations—namely, stem-and-leaf plots, back-to-back stem-and-leaf plots, histograms, and box-and-whisker plots—provides visual insights into the distribution and characteristics of the dataset. The stem-and-leaf plots depict the frequency of specific ages, illustrating distribution patterns, while the back-to-back variant compares distributions between males and females, highlighting gender differences.

The histogram further categorizes the ages into defined groups, facilitating an understanding of age demographics within the family. These visual tools are invaluable for identifying skewness, modality, and outliers in the data, which are critical for accurate descriptive statistics.

Subsequently, the project involves calculating key descriptive statistics for the entire dataset and separately for male and female subsets. Measures such as mean, median, mode, variance, and standard deviation quantify the central tendency and dispersion of ages, offering numerical summaries of the data's distribution. Calculating quartiles and constructing box-and-whisker plots enable a deeper understanding of data spread, identifying median points, quartile ranges, and potential outliers.

Beyond descriptive statistics, the project incorporates probability and counting exercises based on the collected data. These tasks include calculating probabilities of selecting individuals within specific age categories, both experimentally and theoretically, and evaluating the likelihood of sequential events in a hypothetical family scenario, such as selecting people for transportation or estimating market sizes. These exercises foster an understanding of probability concepts, including calculations involving conditional probabilities, sample spaces, and permutations.

The assignment underscores the importance of organized work, clarity in presenting calculations, and thoughtful interpretation of results. By engaging with realistic personal data, students develop a practical grasp of statistical tools and probabilistic reasoning, preparing them for real-world data analysis and decision-making scenarios.

References

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