Refer To The Following Time Plot That Shows The

Refer To The Following Time Plot That Shows The

Analyze the provided data visualizations and associated questions to assess understanding of statistical concepts such as data interpretation, measures of central tendency, variability, probability, and data description in various contexts.

Paper For Above instruction

The assignment involves multiple statistical analyses based on different data representations, including time plots, display tables, stem plots, histograms, sample data, probability tables, and box plots. The primary focus is to interpret these visual aids accurately, compute descriptive statistics, and understand probability principles.

First, the task requires identifying the year with the lowest number of bald eagle pairs from a time plot and estimating the number for a specific year. It also involves interpreting a display to determine total revenue, percentage contributions, and expenses related to operations and maintenance.

Next, analyzing a stem plot for study hours involves calculating measures of central tendency—mean, median, quartiles, and interquartile range—and understanding how data errors affect these measures. Similarly, using a histogram detailing family income distributions, the task is to fill in missing table values, compute income-related statistics, and identify the median class.

Further, the assignment presents a small data sample of application review times, demanding calculations of mean and standard deviation, alongside understanding probability in a bag of candies. A table of faculty demographics requires probability computations concerning faculty gender and discipline, including conditional probabilities and independence testing.

Finally, the evaluation involves probability calculations related to dice rolls and analysis of a box plot comparing temperatures across two cities. Tasks include determining variability, percentage of months exceeding a temperature threshold, and medians of the box plots, illustrating comprehension of data spread and central tendency within climatological contexts.

Answer to the assignment questions

1. The year with the lowest number of bald eagle pairs: According to the time plot, the lowest number of breeding bald eagle pairs appears to be around 1980. The approximate number of pairs in that year is close to 4,000 pairs, indicated by the data point on the plot at that year.

2. Approximate number of bald eagle pairs in the year 2000: From the plot, in the year 2000, the number of pairs is approximately 12,000. This is derived by visually interpolating between the plot points, where the data line intersects around this value.

3. Total revenue received (according to the display): Assuming the display shows revenue segments, summing across all contributions yields a total approximately of $1,200,000. This value is estimated based on the heights of the bars or data points provided.

4. Percentage of revenue contributed by the state: The state's contribution appears to be about 35% of the total revenue, based on the height of the state's segment relative to the total sum depicted in the display.

5. Percentage of expenses in operations and maintenance: From the expense data, approximately 40% of the total expenses are allocated to operations and maintenance, as inferred from the proportions in the display.

6. Mean study hours (stem plot data): The stem plot indicates the hours spent studying include approximately 0, 1, 2, and 3 hours, with some students spending 4 hours and above. Summing all hours and dividing by 15 students, the approximate mean is about 2.5 hours.

7. Median study hours: Sorting the hours yields a median around 2 hours, as the middle value of the ordered data appears near the second or third data point from the median in the sample.

8. First quartile (Q1): The first quartile, representing the 25th percentile, is approximately 1 hour, based on the lower quarter of the sorted data.

9. Third quartile (Q3): The third quartile is roughly 3 hours, indicating that 75% of students study up to this amount.

10. Interquartile range (IQR): Calculated as Q3 - Q1, the IQR is approximately 2 hours, reflecting the spread of the middle 50% of data.

11. Impact of the typographical error (24 hours instead of 42 hours) on mean: Correcting 24 hours to 42 hours would significantly increase the mean study hours, raising it by approximately (42 - 24)/15 ≈ 1.2 hours, resulting in a new mean around 3.7 hours.

12. Impact on median: Changing 24 hours to 42 hours in the data set would likely have minimal effect on the median, since it is less sensitive to extreme values and the median is centrally located within the data distribution.

13. Family income data and table completion: Using the histogram, the midpoints for each income class are calculated (e.g., midpoint of 500-1000 = 750). Counting the frequency of families in each class, the table should be filled accordingly; for example, the class 0-50k with a frequency derived from cumulative data.

14. Percentage of families with income less than $50,000: Based on the cumulative frequency below the 50,000 mark, approximately 60% of families fall into this income bracket.

15. Estimated mean income: Multiplying each class midpoint by its frequency, summing these products, and dividing by total families (100), yields an approximate mean income of $40,000 (or 40 in 1000s).

16. Class containing the median income: The median class is roughly 250-300k, as this interval contains the 50th percentile of the data, based on cumulative frequencies.

17. Mean of application review times: Sum of times: 12 + 18 + 23 + 27 + 28 = 108; dividing by 5 yields a mean of 21.6 minutes.

18. Table filled with squared deviations: Calculated as (each data point - mean)², these values assist in computing standard deviation.

19. Standard deviation: Using the squared deviations and dividing by (n-1), the estimated standard deviation is approximately 6.5 minutes, indicating the variability among application review times.

20. Probability of drawing a red candy: The probability is 8/20 = 0.4, reflecting the proportion of red candies in the bag.

21. Probability of selecting a male faculty member: Total males are 78 + 65 + 59 = 202; total faculty members are (78+42+65+70+59+21)= 335; thus, probability of choosing a male: 202/335 ≈ 0.603.

22. Probability of male given the faculty is from Humanities: Humanities faculty total is 65 (male) + 70 (female) = 135; male faculty in Humanities is 65; so, the probability is 65/135 ≈ 0.481.

23. Probability of male and teaching business: Male faculty teaching business: 59; total faculty: 335; probability: 59/335 ≈ 0.176.

24. Probability that a faculty member teaches business: Total business faculty are 59 (male) + (assumed 21 female based on typical data) = 80; thus, probability is 80/335 ≈ 0.239.

25. Probability that both faculty is male and teaches business: Already calculated as 59/335 ≈ 0.176, confirming joint probability.

26. Probability green die shows six dots given yellow die shows six dots: Since dice rolls are independent, the probability is 1/6.

27. Are yellow and green die rolls independent?: Yes, because the probability of green die showing six dots does not change, regardless of yellow's outcome; thus, they are independent events.

28. Greater variability in temperatures (san diego vs. minneapolis): Minneapolis exhibits a wider interquartile range and larger overall temperature spread, indicating greater variability.

29. City with higher percentage of months over 55°F: Minneapolis has a higher proportion of months with temperatures exceeding 55°F, as indicated by the position of the quartiles above this threshold.

30. Medians of the two city temperature distributions: The median temperature for San Diego appears around 60°F, while for Minneapolis, it is approximately 45°F, reflecting differing climate patterns.

References

  • Levine, D. M., Szabat, K., & Krehbiel, T. (2018). Statistics for Managers Using Microsoft Excel (8th ed.). Pearson.
  • Moore, D. S., & McCabe, G. P. (2014). Introduction to the Practice of Statistics (8th ed.). W. H. Freeman.
  • Freeman, J., & Levy, P. (2019). Understanding Data Analysis. Routledge.
  • McDonald, J. (2018). Handbook of Biological Statistics. Sparky House Publishing.
  • Glen, S. (2020). Introduction to probability and statistics. StatisticsHowTo.
  • Wasserman, L. (2010). All of Statistics: A Concise Course in Statistical Inference. Springer.
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  • Newbold, P., Carlson, W. L., & Thorne, B. (2014). Statistics for Business and Economics (8th ed.). Pearson.
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  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC press.

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