CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
SCHOOL OF BUSINESS AND PUBLIC ADMINISTRATION
Department of Public Policy and Administration
PPA 415 – Research Methods in Public Administration
Exercise 3
1. Do Problems 3.3 and 3.13 in Healey, pp. 82.
Problem 3.3 – You have been observing the local Democratic Party in a large city and have
compiled some information about a small sample of party regulars. Find the appropriate
measure of central tendency for each variable (20 Points Analysis).
Sex
M
M
M
M
M
M
F
F
F
F
M
F
F
Class Years Educ Marital Children
H
32
12th M
5
M
17
12th M
0
L
32
12th Sng 0
L
50
8th W
7
L
25
4th M
4
M
25
12th D
3
H
12th BA
D
3
H
10
BA
Sep
2
M
21
BA
M
1
M
33
BA
M
5
L
37
12th Sng 0
L
15
12th D
0
L
31
8th W
1
Appropriate measure of central tendency
N
Valid
Missing
Sex of
respondent
13
Social class
13
Number of
years in party
13
Education
13
Marital status
13
Number of
children
13
0
0
0
0
0
0
26.15
12.00
2.38
Medium
25.00
12.00
2.00
Mean
Median
Mode
Male
M
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Problem 3.13. PA The data below represent the percentage of workers living in each city
who used public transportation to commute to work in 2000 (20 Points – 15 Analysis, 5
Interpretation).
City
Baltimore
Boston
Chicago
Dallas
Detroit
Houston
Los Angeles
Miami
Minneapolis
New Orleans
New York
Philadelphia
Phoenix
San Antonio
San Diego
San Francisco
Seattle
Washington,
D.C.
Percent
20
32
26
6
9
6
10
11
15
14
53
25
3
4
4
31
18
33
a. Calculate the mean and median of this distribution.
Statistics
Percentage using public transportation
N
Valid
18
Missing
0
Mean
17.78
Median
14.50
b. Compare the mean and median. Which is the higher value? Why?
The mean is the higher value. The distribution has a positive skew because New York has a much
higher usage rate for public transportation.
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c. If you removed New York from this distribution and recalculated, what would happen
to the mean?
Statistics
Percentage using public transportation
N
Valid
17
Missing
0
Mean
15.71
Median
14.00
If you remove New York from the data, the mean drops by 11.6 percent, whereas the median
only falls 3.4 percent. The drop in mean occurs because fully 53 percent of New Yorkers use
public transit. Dropping New York only shifts the median from between New Orleans (14) and
Minneapolis (15) down to New Orleans.
d. Report the mean and median as you would in a formal research report.
Among the eighteen cities in the sample, the mean percentage of the working population that
uses public transportation is 17.78 percent. The corresponding median is 14.5 percent. The
positive skew is due to the high percentage of New Yorkers who use public transportation (53%).
If New York is removed from the sample as an outlier, the mean percentage using public
transportation falls to 15.71, whereas the median changes only to 14 percent.
2. Using the grades.sav data set in SPSS 13.0, calculate the mean, median, and mode
for the five quizzes. On which quiz did students perform the best? On which did
they do the worst? Were any of the quizzes skewed positively or negatively (20
points – 15 Analysis and 5 Interpretation)?
Mean, Median, Mode, Skewness, and Kurtosis for Five Quiz Scores
N
Valid
quiz1
105
Missing
quiz2
105
quiz3
105
quiz4
105
quiz5
105
0
0
0
0
0
Mean
7.47
7.98
7.98
7.80
7.87
Median
8.00
8.00
9.00
8.00
8.00
10
9
10
10
10
-.851
-.656
-1.134
-.919
-.713
.162
-.253
.750
.024
.290
Mode
Skewness
Kurtosis
On the five quizzes, students had fairly consistent results. Because the quizzes measured
the number of correct answers, the mean is the best measure of central tendency. The
highest mean score of 7.98 occurred for quizzes 2 and 3. The lowest mean score of 7.47
occurred on quiz 1. All five quizzes had a negative skew indicating a number of
unusually low scores. The only quick with an abnormally negative skew was quiz 3 with
a skew of -1.134. It was the only quiz with six cases with scores lower than three.
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3. Using SPSS 13.0, answer the following questions:
a. In the Situational Leadership Survey, students were asked to evaluate four
different leadership situations. In each situation, the students had to identify
the development level of the subordinate in the situation and the correct
leadership style to use with them. Calculate the mean, median, and modal
response for “Number of development levels (out of four) correctly predicted
(CorrectDevelopment), “Number of situations (out of four) with correct
actions (CorrectSituation), and “Number of total situations (out of four)
correctly analyzed (CorrectAnalysis).” Overall, how well did the students
analyze the leadership situations (20 points – 15 Analysis and 5
Interpretation)?
Analysis of Development Level and Leadership Style in Four
Leadership Situations
N
Valid
Missing
Number of Development Levels
Correctly Predicted
35
Number of Situations with
Correct Actions
37
Number of Total Situations
Correctly Analyzed
35
4
2
4
Mean
2.49
1.86
1.31
Median
2.00
2.00
1.00
2
1
1
Mode
The situational leadership questionnaire presented four leadership scenarios in which members
of the leadership class were asked to correctly identify the leadership development level of the
subordinate in the scenario and link that development level to the appropriate leadership style.
The average member of the class correctly identified 2.49 (62.3%) of the four development
levels. They correctly recognized only 1.86 (46.5%) of the four appropriate leadership styles.
By the most stringent standard (identifying both the development level and the appropriate style),
the typical leadership student only correctly analyzed 1.31 (35.3%) of the four complete
leadership situations. These results suggest that the class may need more training in the
application of situational leadership theory.
b. Using the Presidential Disaster Decision data set, calculate the mean of
“Presidential Disaster Decision (SBA at Turndowns) [ActionType2].” Using
the MEANS procedure, calculate the same mean for each presidential
administration. Did any presidents grant a significantly greater or lesser
percentage of major disasters (20 Points – 15 Analysis and 5 Interpretation)?
Presidential Disaster Decisions Treating SBA Loan Grants as Turndowns
Administration
Mean
% Difference
N
2.8%
Eisenhower
64.9%
154
4.8%
Kennedy
70.0%
70
3.5%
Johnson
64.4%
135
3.1%
Nixon
68.9%
180
3.6%
Total
66.8%
539
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The four presidential administrations in the disaster decision-making study did not vary
significantly in the rate at which they granted major disasters. The mean percentage granted was
66.8%. The four administrations varied from 64.4% to 70.0%. The average percentage variation
from the mean (assuming all variations as positive) was 3.6%, which is a very small difference.
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