Measures of Variability (Dispersion) and the Normal Curve
PART A: USE SPSS (14 points)
To complete this part of the assignment, you will need to use SPSS for Windows to analyze the data from the 2006 General Social Survey. (SPSS is available in Anspach 251, at the Woldt computer lab, and in the library.) Use the file GSS06PFP-B.sav.
1. Select one interval-ratio variable from the General Social Survey dataset. Tell me the Variable Name and the Variable Label for this variable.
2. Present the appropriate measures of variability (dispersion) for this variable. They are the minimum score, maximum score, range, 25th percentile (Q1), 75th percentile (Q3), interquartile range (IQR), and standard deviation. Create these in SPSS and then print them out either from SPSS or WORD.
3. Discuss what each of these three measures--the RANGE, the IQR, and the STANDARD DEVIATION--tells you about American Adults in 2006 on this variable.
4. Now think about how subgroups of the sample might differ on your variable. Choose one of these three variables to create your subgroups: AGE (recoded into three groups), MARITAL STATUS (recoded into three groups), or CLASS (recoded into two groups). What subgroups are you looking at? Why do you think that these subgroups will differ (or be the same) on your interval-ratio variable?
5. Use the graphic device "the box plot" to compare the ways in which your subgroups differ on your interval-ratio variable. Give the box plot a COMPLETE TITLE. ADD THE SOURCE. Print out the box plot either from SPSS or WORD.
6. Create the mean, median, and IQR on your interval-ratio variable for each of your subgroups in SPSS. Print them out either from SPSS or WORD.
7. Summarize in words the ways in which your subgroups do or do not differ on your interval-ratio variable, given your box plot and your summary statistics (from Questions 5 and 6).
PART B: DO THESE BY HAND (16 points)
8. Here are the number of years of schooling that five people have completed. Calculate the standard deviation. (Show your work so that I can follow you.)
Person 1 12 years
Person 2 15 years
Person 3 10 years
Person 4 16 years
Person 5 14 years
9. Let's say that you were asked to give presentations to two groups of people who had experienced "problems with the police." The idea is to create better community/police relations. You are told that on Monday night the mean age of participants is 16 years old, and the standard deviation is 1 year. On Tuesday night, the mean age of participants is 16 years, and the standard deviation is 8 years. How would you change your two presentations? Which one would be easier to deliver? Why?
10. Let's say that the mean score on an exam is 80 points, and the standard deviation is 5 points. What percentage of students scored above 90 IF the distribution of exam scores forms a normal curve? (You will need the Standard Normal Table, Appendix B in your textbook, to answer this question.)
11. If Joe's exam score is 87, what is his z-score? See details from Question 10. (Show your work so that I can follow you.)
12. What percentage of students scored above Joe? See details from Question 10. (You will need the Standard Normal Table, Appendix B in your textbook, to answer this question.)
13. If Tim's exam score is 77, what percentage of students scored between Joe and Tim? In other words, what percentage of students scored between 77 and 87. See details from Question 10. (Show your work so that I can follow you.) (You will need the Standard Normal Table, Appendix B in your textbook, to answer this question.)
14. What is Sally's percentile rank in the class if she had a score of 82? See details from Question 10. (You will need the Standard Normal Table, Appendix B in your textbook, to answer this question.)
15. The final question is from your textbook. It is Question 14 on page 204. Complete both parts a and b of this question. (You will need the Standard Normal Table, Appendix B in your textbook, to answer this question.)
This assignment is due on Wednesday, October 14.