1. Construct an ungrouped frequency distribution for the ages of study-abroad candidates at their most recent birthday. The data are as follows.
18 20 19 20 20 19 19 19 23 18 20 21 17 20 18 20
2. For the following nominal class intervals, give the real limits and the class in- terval size.
a. 16 b. 60–69 c. 18.00–19.99 d. 12.0–14.9 e. 0–0.4 f. 1.50–1.74
3. For each of the following, give (i) the number of class intervals, (ii) the size of the class interval, and (iii) the nominal limits of the class interval containing the smallest score.
Largest Score Smallest Score Number of Scores
a. 37 8 106
b. 62 23 273
c. 164 126 29
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4. First-line supervisors were asked to complete a job-satisfaction questionnaire. Construct a grouped frequency distribution for the following data.
25 23 18 24 14 21 17 12 19 15 6 22 16 20 20 21 18
5. What are the advantages and disadvantages of grouped and ungrouped frequency distributions?
6. For the job-satisfaction data in Exercise 4, construct a relative frequency distri- bution using % f.
7. Construct a relative frequency distribution for comparing the job satisfaction of assembly-line workers in Exercise 2 in “Check Your Understanding of Section 2.2” with that of first-line supervisors in Exercise 4.
8. Under what conditions is a relative frequency distribution more informative than an ordinary frequency distribution?
9. For the data in Exercise 6 in “Check Your Understanding of Section 2.2,” construct a cumulative frequency distribution.
10. For the first-line supervisors’ data in Exercise 4, construct a cumulative percent- age frequency distribution.
11. a. Students enrolling in Introductory Sociology were randomly assigned to one of three classes: traditional lecture (TL), guided reading (GR), or lecture with multimedia supplements (LM). Following are the class assignments of the students who scored in the top 30 on the final examination; construct a fre- quency distribution for these data.
b. What does your distribution tell you about the relative effectiveness of the classes? LM GR LM TL GR LM LM TL GR LM LM GR TL TL TL LM LM LM GR LM LM LM TL TL LM LM TL GR LM LM
12. Twenty-five physicians were asked what they felt was the main health threat to male executives. The most common responses were occupational stress (OS), obesity (OB), smoking (S), lack of exercise (LE), and other (O). Construct a fre- quency distribution for these data.
OB OS S OB LE S OB OB OS O LE S OS S OB O LE O LE LE OB LE O O OB
13. Toss a die 30 times and construct a frequency distribution showing the number of times each die face occurred.
14. Contrast the procedures for constructing frequency distributions for qualitative variables with those for quantitative variables.
15. Information from a biographical inventory was used to compute a socioeco- nomic index for students in a university marching band. Scores above 72 were classified as very high (VH); scores from 61 to 72, as high (H); scores from 43 to 60, as middle (M); and scores below 43, as low (L). Construct a bar graph for the following data.
H H H H M VH VH H M M L H M VH H H H VH H M M H H VH H M VH H H M M VH M L H VH VH H H M VH M M M VH L M H H VH
16. The value of psychoeducational programs as a means of preventing and relieving problems of daily living is gaining acceptance in the medical community. A health maintenance organization used a questionnaire to survey the health needs of its members. The following table shows the number of respondents who selected one of nine popular programs as the one in which they were most inter- ested. Construct a bar graph for these data. (Suggested by Burnell, George M., and Taylor, Peter H. [1982]. Psychoeducational programs for problems in living.
Health and Social Work,7(1), 7–13.)
Program Number Indicating Primary Interest
Weight reduction 154
Fatigue 101
Marital and sex problems 92
Coping with physical problems 71
Stress 65
Heart disease prevention 61
Assertiveness 60
Stop smoking 48
Headaches 47
17. Research was conducted to investigate “citizen contacting,” in which an indi- vidual approaches government officials or other powerful persons to obtain help for themselves and others. Among the countries surveyed were Austria, the Netherlands, and the United States. The citizens initiating the contacts during the preceding two years were classified according to level of educa- tional achievement. (a) Construct a bar graph for each country for the follow- ing data. (b) What conclusions can you draw from your graphs? (Suggested by Zuckerman, A. S., and West, D. M. [1985]. The political bases of citizen contacting: A cross-national analysis. The American Political Science Review,
2.8 Looking Back: What have you Learned?
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Proportion Making Contact by Level of Education Level of Education
Country 1 (low) 2 3 4 5 6 (high)
Austria .03 .07 .07 .13 .12 .25
Netherlands .04 .09 .11 .21 .25 .23
United States .11 .15 .21 .30 .37 .51
18. Construct a bar graph for the Introductory Sociology data in Exercise 11. 19. Construct a bar graph for the physician data in Exercise 12; plot percentage fre-
quency on the Yaxis.
20. Describe the procedure for constructing a bar graph from a frequency distribution. 21. Construct a pie chart for the Introductory Sociology data in Exercise 11. 22. Construct a pie chart for the socioeconomic data in Exercise 15.
23. Describe the procedure for constructing a pie chart from a frequency distribution. 24. Construct a histogram for the first-line supervisors’ data in Exercise 4. Plot per-
centage frequency on the ordinate.
25. Construct a histogram for the reaction-time data in Exercise 7 in “Check Your Understanding of Section 2.2.” Plot proportionate frequency on the ordinate. 26. How does the construction of histograms and bar graphs differ?
27. Determine the midpoints of the following class intervals. a. 1.50–1.74 b. 100–104 c. 0–2 d. 60–69
28. A study was undertaken to determine how well psychological crises resulting from traumatic events are resolved over time. The participants included 15 female cancer patients who underwent breast surgery for the first time, 15 female patients who underwent less-serious surgery (gall bladder removal, hernia repair, and so forth), and 15 physically healthy (nonsurgery) women. Each patient took the Halpern Crisis Scale at intervals of 0, 3, 7, 11, and 15 weeks. The 0 interval repre- sented the night before surgery. The sample of healthy control participants also took the scale at the same time intervals. The following data, based on the number of women with a Halpern Crisis Scale score over 72, were obtained. A score above 72 is considered a high crisis score. (Suggested by Gottesman, David, and Lewis, Marc S. [1982]. Differences in crisis reactions among cancer and surgery patients. Journal of Consulting and Clinical Psychology,50, 381–388.)
Group Week Number
0 3 7 11 15
Cancer surgery 11 12 14 12 14
Other surgery 8 11 12 10 8
Nonsurgery 4 5 5 6 5
(a) Construct a frequency polygon for these data. Plot the data for each group on the same graph; do not anchor the polygon to the horizontal axis. (b) Write a short paragraph giving your interpretation of these data.
29. Construct a frequency polygon for the first-line supervisors’ data in Exercise 4. Plot percentage frequency on the ordinate.
30. What are the relative merits of histograms and frequency polygons?
31. Construct a cumulative polygon for the reaction-time data in Exercise 7 in “Check Your Understanding of Section 2.2.”
32. (a) Construct a cumulative polygon for the data in Exercise 20 in Section 2.5; plot Cum prop fon the ordinate. (b) Estimate the score below which 50% of the cases fall and the score below which 20% of the cases fall.
33. Data on the prevalence of prostate carcinoma by age range were collected. (a) Construct a relative frequency polygon for the data listed in the following table. (b) Use your polygon to estimate the age at which 50% of men could be expected to have prostrate cancer. (c) One cannot construct a cumulative fre- quency polygon for these data. Explain. (Suggested by Stamey, T. A. [1982]. Cancer of the prostate: An analysis of some important contributions and dilem- mas. Monographs in Urology,3, 65–94.)
Age Group Percent with Disease
90–99 61.3 80–89 38.0 70–79 29.8 60–69 20.5 50–59 11.8 40–49 6.9 30–39 2.1
34. Construct a stem-and-leaf display for the lever-pressing data in Exercise 20 in “Check Your Understanding of Section 2.5.”
35. Indicate whether the following statements are true or false.
a. A distribution that is flatter than the normal distribution is called mesokurtic. b. Leptoin leptokurticmeans slender or narrow.
c. The tail of a negatively skewed distribution extends away from theXand Y
intercept.
d. A distribution with three maximum humps, each with the same frequency, is bimodal.
36. Draw the shape of a frequency polygon that would occur in each of the follow- ing experiments. Identify each distribution.
a. Students at Juilliard School of Music take a test of musical aptitude. b. Students are surprised with a pop quiz immediately after the Easter vacation. c. Participants attempt to solve 20 complex puzzles under five levels of moti-
vation: very low, low, medium, high, and very high.
d. Number of crimes per 1,000 inhabitants is determined for the population of five cities; it turns out that the cities have the same crime rate.
e. The scores for 30 engineering majors and 30 business majors on a test of mechanical aptitude are plotted.
f. Strength of grip is measured for 20 young boys, 20 men in their early 20s, and 20 men over age 65.
g. Arrival time is recorded for people who are late for a concert.
h. The number of persons contracting polio in the United States from 1940 to 1970 is determined from hospital records.
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37. The following data are sales figures for vacuum cleaner salespeople. Prepare graphs that suggest that (a) all the salespeople are producing at a uniformly high level, (b) Chapman should be fired, and (c) they should all be fired.
Chapman $66,000 Hillis $68,200 Hays $67,300 Schmeltekopf $71,000 Daniel $69,900 Lilley $71,100
38. Use a statistical software package to obtain a histogram for the data on first-line supervisors in Exercise 4.
39. Use a statistical software package to obtain a bar graph for the data on physi- cians in Exercise 12.
40. Use a statistical software package to obtain a bar graph for the socioeconomic data in Exercise 15.
41. Use a statistical software package to obtain a histogram for the mechanical- aptitude data in Exercise 6 in “Check Your Understanding of Section 2.2.” 42. Use a statistical software package to obtain a histogram for the reaction-time
data in Exercise 7 in “Check Your Understanding of Section 2.2.”
43. Use a statistical software package to obtain a stem-and-leaf display for the learning data in Exercise 9 in “Check Your Understanding of Section 2.2.” 44. Use a statistical software package to obtain a stem-and-leaf display for the data