CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
SCHOOL OF BUSINESS AND PUBLIC ADMINISTRATION
Department of Public Policy and Administration
PPA 415 – Research Methods in Public Administration
Exercise 4
1. Do Problems 4.3, 4.8, and 4.12 in Healey (p. 97-99).
Problem 4.3. In problem 3.1 at the end of chapter 3, you calculated measures of central
tendency for six variables from freshmen and seniors. Three of those variables are
reproduced here. Calculate mean, range, and standard deviation for each variable for
each class. Write a paragraph summarizing the differences between freshmen and
seniors.
Table 1. Expenses and Entertainment Choices by Class Level
Student Class Level
Freshman
Senior
N
10
Range
$32
Mean
$48.50
Std. Deviation
$9.710
10
14
5.80
5.329
10
10
5.50
3.536
11
$50
$63.00
$15.931
11
14
5.18
4.238
Rating of Cafeteria Food
11
8
4.55
2.622
Valid N (listwise)
11
Out-of-Pocket Expenses
Number of Movies
Rating of Cafeteria Food
Valid N (listwise)
10
Out-of-Pocket Expenses
Number of Movies
Based on the information from the survey, freshmen have 77 percent of the out-of-pocket
expenses of seniors. On the other hand, seniors’ expenses vary 64 percent more on average
than freshmen’s expenses. Freshmen also see slightly more movies (5.8 to 5.2) than seniors,
and rate cafeteria food higher (5.5 versus 4.6). However, these latter differences are not
significant.
Problem 4.8. Per capita expenditures for police protection for 20 cities are reported
below for 1995 and 2000 in dollars. Compute a mean and standard deviation for each
year, and describe the differences in expenditures for the five-year period. As an
option, find the range and interquartile range for each year.
Table 2. Summary Statistics on Police Protection Expenditures, 1995 - 2000
Per Capita 1995
Per Capita 2000
Police Protection
Police Protection
Expenditures
Expenditures
N
20
20
Mean
101.00
158.60
Std. Deviation
30.58
46.34
Range
128.00
161.00
Percentiles
25
85.50
124.25
50
99.50
145.50
75
113.00
200.75
Interquartile
Range
P75 - P25
27.50
76.50
Between 1995 and 2000, average police protection expenditures increased from $101.00 to
$158.60, a 57 percent increase. The average variation in expenditures across cities also
increased from $30.58 to $46.34 dollars, a 51 percent increase in variation. This increase in
variation is also picked up by the interquartile range, which increased from $27.50 to $76.50.
Problem 4.12. You’re the governor of the state and must decide which of four
metropolitan police departments will win the annual award for efficiency. The
performance of each department is summarized in monthly arrest statistics as reported
below. Which department will win the award? Why?
Table 3. Arrest Efficiency – Metro Police Departments
Departments
A
B
C
Mean Arrests
601.30 633.17 592.70
St. Dev.
2.30
27.32
40.17
Coefficient of Variation
0.4%
4.3%
6.8%
D
599.99
60.23
10.0%
The standard of efficiency suggests that the metropolitan police department with highest
arrest statistics coupled with the least variation across months would be the most efficient
and should receive the award. One way of measuring this would be to calculate the
coefficient of variation (CV) for each department. The department with the lowest
coefficient would be the most efficient department. The coefficient of variation is the
standard deviation divided by the mean (expressed as a percentage). The department with
lowest coefficient of variation (and the lowest standard deviation) is Department A, which
should receive the award.
2. Do Exercise 3 in Chapter 7 of George and Mallery (p. 104).
Table 4. Descriptive Statistics for George & Mallery, Chapter 7, Exercise 3
VAR1
N
10
Mean
4.70
Std. Deviation
2.359
Variance
5.567
VAR2
10
4.70
2.584
6.678
VAR3
10
5.30
2.497
6.233
Valid N (listwise)
10
3. In 1999, University of Alabama at Birmingham conducted a needs assessment survey
with residents of public housing provided by the Jefferson County Housing Authority.
The respondents reported annual income in the following ranges:
Table 5. Jefferson County Housing Authority Survey 1999. Respondent Income Ranges
Frequency
Valid
Percent
Valid Percent
Cumulative
Percent
$0 to $5,000
60
32.4
32.4
32.4
$5,000 to $10,000
74
40.0
40.0
72.4
$10,000 to $15,000
22
11.9
11.9
84.3
$15,000 to $20,000
8
4.3
4.3
88.6
100.0
$20,000 and up
Total
21
11.4
11.4
185
100.0
100.0
Assuming that you have only the frequency distribution above as information, estimate
the (grouped) mean, median, mode, and standard deviation for income among JCHA
residents in 1999.
Table 6. Summary Statistics, Income, JCHA 1999
N
185
Mean
Median
Mode
Std. Deviation
$8,608.11
$7,164.18(a)
$7,500
$6,319.328
a Calculated from grouped data.
4. Using SPSS 13.0, run frequency distributions for the following variables:
a. In the Disaster Declarations, 1953 – 1973, data set, run the frequency and
calculate the index of qualitative variation (by hand) for primary disaster type
(PrimaryDisasterType). Interpret the results. How even or uneven is the
distribution? What does evenness or unevenness of the distribution mean?
Table 7. Primary Disaster Type, 1953 - 1973 - Index of Qualitative Variation
Primary Disaster Type
Earthquake
Winds, Tornadoes and Flooding
Flooding, Storm Surge, Tsunamis, Landslides
Windstorms, Hurricanes, and Tornadoes
Commercial Failures Caused by Climate and Environment
Forest Fire, Brush Fire, Wildfire, Fire
Drought
Snow Storm, Ice Storm, Winter Weather
Riots, Chemical Accidents, Explosions, Insect Infestations
Total
Valid
Cumulative
2
Percent
Frequency Frequency Percent Percent
5
25
0.9
0.9
0.9
29
841
5.4
5.4
6.3
322
103684
59.7
59.7
66.0
110
12100
20.4
20.4
86.5
6
36
1.1
1.1
87.6
16
256
3.0
3.0
90.5
15
225
2.8
2.8
93.3
22
484
4.1
4.1
97.4
14
196
2.6
2.6
100.0
539
117847
100.0
100.0
k=
N2 =
k(N2 - Σf2)
N2(k-1)
IQV=
9
290521
1554066
2324168
66.9%
The distribution of primary disaster type for the period 1953 to 1973 is highly skewed. Fully 80.2
percent of the cases fall into the two categories of flooding and windstorms. As a result, the
Index of Qualitative Variation (IQV) is 66.9 percent of the maximum variation that would be
present if all types of disaster were equally probable.
b. In the Leadership Skills data set, run Frequencies and Descriptives to calculate the
mean, median, mode, standard deviation, range, and interquartile range for the
three summary variables, Technical Skills, Human Skills, and Conceptual Skills.
Interpret the results. On what skills do the respondents rate themselves highest
and lowest? On what leadership skills do the respondents have the most
consistent (least varying) opinions? On what leadership skills do they have the
least consistent (most varying opinions)?
Table 8. Leadership Skills Scales
Technical Skills
Scale
N
Mean
Median
Mode
Std.
Deviation
Range
Percentiles
IQR (P75-P25)
a
41
26.3
27.0
27.0
Human
Skills
Scale
41
25.3
25.0
25.0
Conceptual
Skills Scale
41
24.0
24.0
22.0
2.6
2.7
11.0
11.0
25
25.0
23.5
50
27.0
25.0
75
28.0
27.0
3.0
3.5
Multiple modes exist. The smallest value is
shown
3.2
12.0
22.0
24.0
27.0
5.0
Generally speaking, the mean, median, and mode all suggest that students in the leadership class
were more confident in the level of their technical skills than they were in their human and
conceptual skills. The simpler and more straightforward the skill, the more likely it was that
leadership students rated themselves highly on it. The more complex and abstract was the skill,
the less confidence students expressed in their own abilities. The indecision in their rankings is
reflected in the increasing standard deviations and interquartile ranges across the three rankings.