Standard Deviation and Outliers

Thread:

For this assignment you will use the Project 2 Excel Spreadsheet to answer the questions below.

Use the spreadsheet to create the graphs as described in each question and then answer the question.

Put all of your answers into a post in the Project 2 Discussion Board Forum.

This course will be utilizing the Post-First feature. You will not be able to see your classmates' posts until after you have made your own post. 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 2nd post for any of your answers to questions 1-5, you must get permission from your instructor.

1. a) Create a set of 5 points that are very close together and record the standard deviation. Next, add a 6th 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 what happened to the standard deviation in words. 

b) 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 2nd 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? 

1. Go back to the spreadsheet and clear the data values from question 1 from the data column and then put values matching the following data set into the data column for the first graph. 

50, 50, 50, 50, 50. 

Notice that the standard deviation is 0. Explain why the standard deviation for this one is zero. Do not show the calculation. Explain in words why the standard deviation is zero when all of the points are the same. If you don't know why, try doing the calculation by hand to see what is happening. If that does not make it clear, try doing a little research on standard deviation and see what it is measuring and then look again at the data set for this question.

1. Go back to the spreadsheet one last time and put each of the following three data sets into one of the graphs. Record what the standard deviation is for each data set and answer the questions below.

                        Data set 1:        0, 25, 50, 75, 100

                        Data set 2:        30, 40, 50, 60, 70

                        Data set 3:        40, 45, 50, 55, 60

Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists. Do not give your calculations in your answer - explain in words.  (8 points)

For the last 2 questions, use the Project 1 Data set that is found in Course Content >> Syllabus and Assignment Instructions >> Assignment Instructions in Blackboard.

• Explain what an outlier is. Then, if there are any outliers in the Project 1 Data Set, what are they? If there are no outliers, say no outliers.  (4 points)
• Which 4 temperatures in the data set look to be the most questionable or the most unrealistic to you? Explain why you selected these 4 points. (4 points)

Replies:

After you have made your post, you will be able to see your classmates' posts. Find 2 classmates who disagreed with at least some part of at least one of your answers to questions 4 and 5 and explain why your answers are correct. If after reading some of your classmates' posts, you change your mind about the right answers for questions 4 and 5, explain what you were thinking originally as well as what you think now and why.

(8 points)

• Submit your answers to these questions by 11:59 p.m. (ET) on Saturday of Module/Week 3. Submit your 2 replies of at least 50 words each by 11:59 p.m. (ET) on Monday of Module/Week 3.