What are the means? The standard deviations? Compare the mean with the standard deviation for each variable. Does there appear to be more variability in the crimes or in police expenditures per capita in these states? Which states contribute more to this greater variability? nzzieHoniltonThe SPSS output showing the mean and the standard deviation for both variables is presentedbelow.Number of Crimes per100,000 PopulationPolice ProtectionExpenditures (in millionsof dollars)Valid N (listwise)NDescriptive Statistics212121Minimum2181120Maximum Mean Std. Deviation41883038.90583.0048164 1703.951895.214a. What are the means? The standard deviations?b. Compare the mean with the standard deviation for each variable. Does there appear tobe more variability in the number of crimes or in police expenditures per capita in thesestates? Which states contribute more to this greater variability?il diffamsc. Suggest why one variable has more variability than the other. In other words, what socialforces would cause one variable to have a relatively large standard deviation? es ofutionith athe12-w.five categories (DEGREE).for respondent's age when first child was born (AGEKDBRN) is reported forIdentify the level of measurement for DEGREE and AGEKDBRN.a.b. Describe the relationship between respondent degree and age when first child was born.MeanStandard deviationVarianceStateMaineNew HampshireVermontMassachusettsRhode IslandConnecticutNew YorkNew JerseyPennsylvaniaLess ThanHigh SchoolOhioIndianaIllinoisMichiganWisconsinMinnesota20.72lowaMissouriNorth DakotaSouth DakotaNebraskaKansas4.74522.512HighSchool23.345.54230,709SomeCollege23.469. You are interested in studying the variability of crimes committed (including violent andproperty crimes) and police expenditures in the eastern and Midwestern United States. TheU.S. Census Bureau collected the following statistics on these two variables for 21 states inthe East and Midwest in 2008.Number of Crimes per100,000 Population5.57531.082Police Protection Expenditures(in Millions of Dollars)2,5832332,3843172,7611412,8601,8433,0983172,7989962,4078,1642,6183,0872,8422,8403,9823,1573,9471,2233,4984,2423,4922,4253,0471,5522,8931,5272,8206144,1881,6322,3431202,1811415283,2756843,800Source: U.S. Census Bureau, Statistical Abstract of the United States: 2012, Tables 308 and 443.Notes:Bachelor'sDegree27.98a. Limited data for Illinois during 2008 were available.b. Limited data for Minnesota during 2008 were available.6.18538.259GraduateDegree28.996.20538.496CHAPTER 4 Measures of Variability

Given the data of 21 states in the East and Midwest collected by U.S. Census Bureau for studying the…

Answered: What are the means? The standard…

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What are the means? The standard deviations? Compare the mean with the standard deviation for each variable. Does there appear to be more variability in the crimes or in police expenditures per capita in these states? Which states contribute more to this greater variability?

nz
zie
Hon
ilton
The SPSS output showing the mean and the standard deviation for both variables is presented
below.
Number of Crimes per
100,000 Population
Police Protection
Expenditures (in millions
of dollars)
Valid N (listwise)
N
Descriptive Statistics
21
21
21
Minimum
2181
120
Maximum Mean Std. Deviation
4188
3038.90
583.004
8164 1703.95
1895.214
a. What are the means? The standard deviations?
b. Compare the mean with the standard deviation for each variable. Does there appear to
be more variability in the number of crimes or in police expenditures per capita in these
states? Which states contribute more to this greater variability?
il diffams
c. Suggest why one variable has more variability than the other. In other words, what social
forces would cause one variable to have a relatively large standard deviation?

es of
ution
ith a
the
12-
w.
five categories (DEGREE).
for respondent's age when first child was born (AGEKDBRN) is reported for
Identify the level of measurement for DEGREE and AGEKDBRN.
a.
b. Describe the relationship between respondent degree and age when first child was born.
Mean
Standard deviation
Variance
State
Maine
New Hampshire
Vermont
Massachusetts
Rhode Island
Connecticut
New York
New Jersey
Pennsylvania
Less Than
High School
Ohio
Indiana
Illinois
Michigan
Wisconsin
Minnesota
20.72
lowa
Missouri
North Dakota
South Dakota
Nebraska
Kansas
4.745
22.512
High
School
23.34
5.542
30,709
Some
College
23.46
9. You are interested in studying the variability of crimes committed (including violent and
property crimes) and police expenditures in the eastern and Midwestern United States. The
U.S. Census Bureau collected the following statistics on these two variables for 21 states in
the East and Midwest in 2008.
Number of Crimes per
100,000 Population
5.575
31.082
Police Protection Expenditures
(in Millions of Dollars)
2,583
233
2,384
317
2,761
141
2,860
1,843
3,098
317
2,798
996
2,407
8,164
2,618
3,087
2,842
2,840
3,982
3,157
3,947
1,223
3,498
4,242
3,492
2,425
3,047
1,552
2,893
1,527
2,820
614
4,188
1,632
2,343
120
2,181
141
528
3,275
684
3,800
Source: U.S. Census Bureau, Statistical Abstract of the United States: 2012, Tables 308 and 443.
Notes:
Bachelor's
Degree
27.98
a. Limited data for Illinois during 2008 were available.
b. Limited data for Minnesota during 2008 were available.
6.185
38.259
Graduate
Degree
28.99
6.205
38.496
CHAPTER 4 Measures of Variability

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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