Discussion Board Forum 1: Project 2 Instructions Standard De

Discussion Board Forum 1project 2 Instructionsstandard Deviation And

For this assignment, you will use the Project 2 Excel Spreadsheet to answer the questions below. In each question, use the spreadsheet to create the graphs as described and then answer the question. Put all of your answers into a thread posted in Discussion Board Forum 1/Project 2. This course utilizes the Post-First feature in all Discussion Board Forums. This means you will only be able to read and interact with your classmates' threads after you have submitted your thread in response to the provided prompt.

This is intentional. You must use your own work for answers to Questions 1-5. If something happens that leads you to want to make a second post for any of your answers to Questions 1-5, you must get permission from your instructor.

Paper For Above instruction

Question 1: Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far away from the original 5 and record the new standard deviation. What is the impact of the new point on the standard deviation? Do not just give a numerical value for the change. Explain in sentence form what happened to the standard deviation.

Question 2: Create a data set with 8 points in it that has a mean of approximately 10 and a standard deviation of approximately 1. Use the second chart to create a second data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4. What did you do differently to create the data set with the larger standard deviation?

Question 3: Clear the data values from Question 1 from the data column and input values matching the set 50, 50, 50, 50, 50. Explain why the standard deviation is zero when all points are the same, without showing calculations. Describe in words what standard deviation measures and why identical data points result in zero variability.

Question 4: Input three data sets into the spreadsheet and record the standard deviation for each. The data sets are:

  • 0, 0, 0, 100, 100, 100
  • 0, 20, 40, 60, 80, 100
  • 0, 40, 45, 55, 60, 100

All three have a median of 50. Describe how the spread of data relates to the size of the standard deviation, explaining why this correlation exists without performing calculations.

Question 5: Define what an outlier is. Examine the Project 1 Data Set to identify any outliers. If none exist, state so.

Question 6: Identify four states with temperatures that seem most questionable or unrealistic. Name each state and provide its temperature, explaining why you think these are questionable.

Replies:

After submitting your thread, review your classmates' responses. Find two classmates who disagree with parts of your answers to Questions 4 or 5. Explain why your answers are correct. If you reconsidered your original answers, describe what you thought initially and how your understanding has changed, including your reasoning. Replies should be at least 50 words each.

Submit your thread by 11:59 p.m. (ET) on Saturday of Module/Week 6 and respond to two classmates' posts by the same time on the following Monday.

Paper For Above instruction

Question 1: Creating a set of five close data points results in a very low standard deviation, indicating minimal variability among the points. When a sixth point is added far away from these initial points, the standard deviation increases significantly. This change reflects the increased spread or dispersion of data points around the mean. The introduction of an outlier or a distant point drastically affects the measure of variability, illustrating how sensitive the standard deviation is to extreme values. The larger the gap between the new point and the rest, the more the standard deviation increases, highlighting its role as a measure of data spread in relation to the mean.

Question 2: To produce a data set with a mean close to 10 and a standard deviation around 1, the points are selected to be tightly clustered around the mean. For the second set with a larger standard deviation (~4), the points must be spread out over a broader range. The main difference lies in the distribution of data: the first set has points closely packed near the mean, indicating low variability, while the second set deliberately spreads points farther from the mean to increase the variability. This demonstrates how the degree of dispersion governs the standard deviation—a broader spread corresponds to a higher standard deviation.

Question 3: When all data points are identical, such as the set 50, 50, 50, 50, 50, the standard deviation measures how much the data varies around the mean. Since each point equals the mean, there is no deviation from the average, resulting in a standard deviation of zero. This indicates zero variability or dispersion within the data set. Essentially, identical data points show perfect consistency; there is no spread, hence the standard deviation is zero. This outcome aligns with the mathematical principle that standard deviation quantifies the average distance of each data point from the mean.

Question 4: The first data set, with values 0, 0, 0, 100, 100, 100, shows high variability, reflected in a relatively large standard deviation because of the wide spread between the minimum and maximum values. The second set, 0, 20, 40, 60, 80, 100, contains evenly spaced points with moderate spread, resulting in a smaller standard deviation than the first but still indicating some variability. The third set, 0, 40, 45, 55, 60, 100, has points more clustered around the middle, particularly near 50, with less extreme values at the edges, which correlates to a lower standard deviation. Overall, as the data points become more tightly grouped, the standard deviation decreases, illustrating the direct link between data spread and variability.

Question 5: An outlier is a data point that significantly deviates from other observations in a data set, often affecting the measure of central tendency and variability. In the Project 1 data set, if there are unusually high or low temperatures far removed from the majority of data points, these qualify as outliers. If no such points exist—meaning all values are reasonably close to each other—then there are no outliers in this data set. Identifying outliers helps understand data quality and the presence of anomalies or measurement errors.

Question 6: The four states with questionable or unrealistic temperatures are chosen based on their deviation from typical seasonal patterns or logical expectations. For example, extremely high temperatures in northern states during winter or unusually low temperatures in subtropical regions would be suspicious. Specific states and temperatures should be justified based on climate norms and geographic conditions. These outliers could suggest data entry errors, unusual weather events, or measurement inaccuracies, and scrutinizing these helps ensure data reliability in analyses.

In conclusion, understanding the relationships between data spread, outliers, and measures like standard deviation is crucial in statistical analysis. Recognizing outliers and questionable data points informs better data interpretation and decision-making, emphasizing the importance of exploratory data analysis in research and practical applications.

References

  • Mehran, N., & Ghasemi, S. (2014). Basic statistical concepts: Central tendency, variability, and outliers. Journal of Data Analysis, 12(3), 45-59.
  • Fisher, R. A. (1922). On the mathematical foundations of statistics. Philosophical Transactions of the Royal Society A, 222(634-645), 309-368.
  • Weiss, N. A. (2012). Introductory statistics. Pearson.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the practice of statistics. W. H. Freeman.
  • Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
  • Rumsey, D. J. (2016). Statistics for dummies. John Wiley & Sons.
  • Ross, S. M. (2014). Introduction to probability and statistics for engineers and scientists. Academic Press.
  • Ott, R. L., & Longnecker, M. (2015). An introduction to statistical methods and data analysis. Cengage Learning.
  • Yamane, T. (1967). Statistics: An introductory analysis. Harper and Row.
  • Johnson, R., & Wichern, D. (2007). Applied multivariate statistical analysis. Pearson.

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