Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual

Preview (31 of 137 Pages)

100%

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 1 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionChapter 1–Answers toAll Exercises1.Once our research question, the hypothesis, and the study variables have been selected, we move onto the next stage of the research process–measuring and collecting the data. The choice of a particulardata collection method or instrument depends to our study objective. After our data have beencollected, we have to find a systematic way to organize and analyze our data and set up some set ofprocedures to decide what we mean.2.a.Females have less education than males; males retire at a greater age than females.b.Whites have greater incomes than any other race. Hispanics have incomes greater than blacks butless than whites.c.As the number of police in a city increases, the crime rate will decrease.d.Life satisfaction may vary with marital status, with satisfaction higher among married personsthan those not married.e.As military expenditures as a percentage of GNP increase, the overall level of security maydecrease, as witnessed by many Third World countries, or in the troubled Middle East. In fact,military expenditures (except during the Cold War) often increasebecauseof rising conflict, butthose expenditures may or may not guarantee more security.f.Minorities are more likely to care for their elderly parents than non-minorities.3.a. Interval ratiob. Nominalc. Interval ratiod. Ordinale. Nominalf. Interval ratiog. Interval ratioh. Nominal4.a. Discretec. Continuousf.Discreteg. Continuous5.There are many possible variables from which to choose. Some of the most common selections bystudents will probably be: type of occupation or industry, work experience, and educational trainingor expertise. Students should first address the relationship between these variables and gender. Forexample, Men have more years of work experience than women in the same occupation. Student mayalso consider measuring structural bias or discrimination.6.a.Unemployment records could be used to determine the actual number of unemployed; adescriptive statistic based upon the population.b.A survey is taken to estimate student opinions about the quality of food; inferential statistic.c.National health records can be used to determine the incidence rate of breast cancer among allAsian women, so this would be a descriptive statistic.d.The ratings will be gathered from a survey, so this is inferential.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 2 preview image

Loading page ...

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 3 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editione.A university should be able to report GPA by major, so this is a descriptive statistic based uponthe population.f.In theory, the U.S. records accurately all immigrants to this country. Therefore, the number ofSouth East Asian immigrants would be a descriptive statistic. However, because of illegalimmigration,surveys are also taken to estimate the total number oflegal and unauthorizedimmigrants. In that event, the number of immigrants would be an inferential statistic.7.In general, the difficulty with studying criminal acts is that the criminal act needs to be reportedfirst. It is estimated that the majority of crimes are not reported to authorities. Data on reportedcrimes are routinely collected by the Federal Bureau of Investigation and the Bureau of Justice.8.At the nominal level, a simple measure of political participation is whether or not someone voted inthe most recent general election. This variable would be coded either “yes” or “no.”At the ordinal level, a composite measure could be constructed of both voting and political partymembership, like this:BehaviorCodeDidn’t vote, no membership0Voted, no membershipOR Membership, didn’t vote1Voted and membership2These codes are ordinal in scale because the amount of political participation can be ranked from highto low. Other possible ordinalvariables can be constructed from other sets of behaviors, such asworking in a candidate’s campaign, signing a petition, and so forth. The key points are to create avariable whose values can be ranked and whose values are not on an interval-ratio scale.At the interval-ratio level, political participation could be measured by the percentage of elections inwhich a person has voted since becoming eligible to vote, or the amount of money a persondonated to political candidates during some specified time period.9.Individual age: This variable could be measured as an interval-ratio variable, with actual age in yearsreported. As discussed in the chapter, interval ratio variables are the highest level of measurement and canalso be measured at ordinal or nominal levels.Annual income: This variable could be measured as an interval-ratio variable, with actual dollar earningsreported.Religiosity: This variable could be measured in several ways. For example, as church attendance, thevariable could be ordinal (number of times attended church in a month: every week, at least twice a month,less than two times a month, none at all).Student performance: This could be measured as an interval-ratio variable as GPA or test score.Social class: This variable is an ordinal variable, with categories low, working, middle and upper.Attitude toward gun control: This variable is an ordinal variable, with categories strongly disagree,disagree, neutral, agree and strongly agree.SPSS SolutionsNA

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 4 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 5 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionChapter 2–Answers to Exercises (in-text)1.a.Race is a nominal variable. Class is an ordinal variable, since the categories can be ordered fromlower to higher status.b.Frequency Table for RaceRaceFrequency (f)White17Nonwhite13Total (N)30Frequency Table for ClassClassFrequency (f)Lower3Working15Middle11Upper1Total (N)302.ClassPercentageLower10.0%Working50.0%Middle36.7%Upper3.3%Total100%a.The smallest perceived class is the upperclass, composing only 3.3% of the survey.b.Together, the working and middle class compose 86.7% of the survey.3.Number of traumasFrequency (f)01511124Total (N)30Trauma is an interval or ratio-level variable, since it has a real zero point and a meaningful numeric scale.b.People in this survey are more likely to have experienced no traumas last year (50% of the group).c.The proportion who experienced one or more traumas is calculated by first adding 36.7% and 13.3% =50%. Then divide that number by 100 to obtain the proportion, 0.50, or half the group.4.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 6 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionWhite57%Nonwhite43%Lower10%Working50%Middle37%Upper3%

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 7 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition5.Ranking them from highest to lowest level of support: Strong Democrats, StrongRepublicans andIndependents. Support does vary by group, however, the majority of strong Democrats (56.8%) and strongRepublicans (50%) agree/strongly agree with the statement. The group with the lowest level of support isIndependents with 42.3%.6.Email hoursper weekFrequencyCf%C%019191919120392039213521352355755742592595665665657057072722728375375917617610 or more23992399Total9999%b..575 (57/99) spent 3 hours orless on email per week.c.This group includes 5+2+3+1+23= 34 respondents. The proportion is 34/99 or .343.d.A histogram can be used to display frequency for an interval variable.0246810121416012

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 8 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition7.a.For whites.Educationf%C%Less than high school7212.312.3High school graduate27246.558.8Junior college467.966.7Bachelor11820.286.9Graduate7713.2100.1TOTAL585For blacks.Educationf%C%Less than high school2622.022.0High school graduate595072.0Junior college108.580.5Bachelor1613.694.1Graduate75.9100.0TOTAL1180510152025012345678910

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 9 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionFor males.Educationf%C%Less than high school4614.014.0High school graduate15145.959.9Junior college247.367.2Bachelor6519.887Graduate4313.1100.1TOTAL329For females.Educationf%C%Less than high school6715.015.0High school graduate21447.862.8Junior college378.271.0Bachelor8118.189.1Graduate4910.9100.0TOTAL448b.40.2% of males attended school beyond high school.A lower percentage of females (37.2%) did thesame.c.58.8% for whites and 72.0% for blacks.d.Cumulative percentages are more similar for men and women than for white and blacks. Inequalityappears to be larger between racial groups. A larger percentage of whites complete bachelor or graduatedegrees than do blacks.8.a.We can conclude the highest rate of uninsured is in the following categories: 18-44 years of age,100-199% of the poverty level, American Indian or Alaska Native only, and South and Westgeographic regions.b. Pie charts can be used to compare the demographic data. However, age and percent of poverty levelare ordinal measures and can be presented in histograms.9.The group with the largest increase in voting rates is blacks, from 53% in 1996 to 66.2% in 2012. Blacksare the only group that did not experience a decline in voting rates for the years presented.Hispanic voting rates exceeded the voting rates for Asians in 2000 and remained higher thanAsians through 2012. Hispanics and Asians have the lowest voting rates for all groups. As notedin the exercise, in the 2012 presidential election, blacks had the highest voting rates for all groups,followed by non-Hispanic whites, Hispanics and Asians. White voting rates declined by 2% from2008 to 2012. The highest voting rate for whites was in 2004 (67.2%), 2008 for Hispanics (49.9%)and for Asians (47.6%).

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 10 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition10.b.The shapes of both histograms are similar, which indicates that both groups have roughly thesame type of distribution of educational attainment. The highest percentage of blacks is in the 9-12 category, while the highest percentage of whites is in the next category, 13-16 years.Whiteshave higher educational attainment, 15.4% of whites vs. 9.3% of blacks completed 17-20 years ofeducation.11.a.Victimization rates are highest for those 12-17 years of age.b.Victimization rates have been declining since 1994-1998.In the last time period, 2005-2010, allrates are below 5 per 1,000 females. Across the three time periods, victimization rates are highestfor females age 12-17 (11.3 to 4.1). Second highest rates are among females age 18-34 year (7.0 to3.7).12.For sex and age: Women were more likely than men to indicate that same-sex marriage should belegal. There was an increase in both age groups for men and women. The highest increase was among menages 18-49 years. For age: There is an increase in support across all three age groups. The largest increasewas among those 18-34 years of age (70-54 = 16%). For political affiliation: There was an increase in thepercent indicating support for the legalization of same-sex marriage among Democrats and Independents.No change among Republicans. For political views: There was an increase in support for same-sex marriageamong all political affiliation categories. The percent increases can be ranked from high to low: moderates(9%), liberals (8%) and conservatives (3%).13.The group with the highest level of support (favor) for stricter gun laws is graduate degree(84.4%), followed by the high school degree group (77.02%). The lowest level of support is reported forthe junior college group (71.43%).14.a.The variable PAYHLTH is an ordinal level measurement.b.A higher percentage of women (63.2%) than men (55.7%) indicated that they stronglyagree or agree to the statement. Based on these responses, women are more likely to be worried aboutreceiving second-class health care than men.0510152025303540450-45-89-1213-1617-20WhitesBlacks

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 11 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionChapter 2SPSS Solutions1.a.15.8% of the sample is divorced.b.47.8% are married.c.Currently single includes those in the following response categories: widowed, divorced, andnever married: 8.9 + 15.8 + 24.6 = 49.3%2.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 12 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionb.Each variable is an ordinal measurement. [Review the definitions of levels of measurement.] Thehigher value (5) indicates strong disagreement to the statement.Overall, respondents expresspositive attitudes toward immigrants. Most believe that immigrants are good for America (48.6%agree or strongly agree to the statement) and disagree that immigrants increase crime rates (46%disagree or strongly disagree). However, almost 41.7% agree or strongly agree that immigrantstake away jobs.3.a.RACIDIMP is an ordinal measure (a four point scale).b.RACIDIMP may vary by respondent’s racial identity (RACECEN1 and RACECEN2),whether the respondent lives in racially diverse neighborhood (RACLIVE) or the number offamily generations in the household (FAMGEN).4.Students are encouraged to determine on their own how to recode the variable.Students shouldconsider how the years of education is related to degree attainment, for example: 12 years = high schoolgraduate or 16 years = college graduate.5.We recoded labor force participation rates into four categories: 1–25% and below, 2–25.01-50%, 3–50.01-75% and 4–75.01% and above. Our recoded variables are presented in the following tables.From the data we can conclude that labor participation is higher for males than females. There were nocountries where the male labor force participation rate was 50% or less. Out of the 70 countries, all the

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 13 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionreported labor rate was 50.01% or higher. The largest category was 50.01-75 (75.7% of all cases). For women,the largest category was 50.01-75% (60% of all cases).6.a.Bar graph for AGEGRPA

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 14 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionb. Bar graphs for males and females (% of cases reported)

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 15 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionc.Overall, almost two third of the respondents are above 45. The largest age category for both male andfemale respondents is the oldest group, 45+. A slightly higher percent of males are 45 or older (74.91%) thanthe females (65.7%). The second largest age group is the youngest one, 18-34. 17.38% of the femalerespondents fall in this category as compared to their male counterparts of whom 12.37% are between 18 to34 years of age.7.The amount of respondents who have ever looked for information about health or medical topics from anysource increases as educational degree increases, from 44.4% among those with less than 8 years ofeducation to 93.1% among those with a postgraduate degree.You can see the increase in this category bytracking how the blue section of the pie chart increases in size with each educational level.8.a. GeneralHealth(Bar Chart). Approximately the same percent of men and women report excellent, verygood and good health. A slightly higher percentage of males report fair health (13.1 vs. 11.9%) thanwomen and slightly more women report poor health (3.4 vs. 2.9%) than women.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 16 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionb.Occupation Status (Bar Chart).A higher percentage of males are employed than females (57.12% vs. 51.73%The largest difference between the two groups is in the “Homemaker” category in which 10.61% of thefemale respondents fall as compared to only 0.178% of their male counterparts.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 17 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionc.EverHadCancer (Pie Chart). A slightly higher percentage of men reported that they have been diagnosed ashaving cancer than women, 14.8% vs. 13.9%

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 18 preview image

Loading page ...

Frankfort-Nachmiasand Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition9.RentOrOwn: nominalWhenDiagnosedCancer: intervalIncomeRanges-ordinalQualityCare: ordinalInterval data is best displayed in histograms, while ordinal and nominal data can be displayed in pie chartsor bar graphs.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 19 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionCHAPTER 3 SPSS PROBLEMS SOLUTIONS* Selected, but not all, output is shown below with some graphic modification.1.a.Looking at the following frequency distribution, the variable HOMOSEX is measuredat the ordinal level. Therefore, the median isthe appropriate measure of centraltendency because the mean can only be used with interval-ratio variables. In this case,the median is “Always Wrong.”b.The following frequency distributions contains information on attitudes towardshomosexual relations for men and women:Men:Women:

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 20 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionFrom the tables above, it appears that men and women have pretty similar attitudes onhomosexual relations. That is, 51.7 percent of men and 49.2 percent of women saythat homosexual relations are“Always Wrong.” Additionally, 35.4 percent of menand 38.5 percent of women say that homosexual relations are “Not Wrong at All.”And, about 13 percent of men and 12 percent of women are somewhere in the middlesaying that homosexual relations are either “Almost Always Wrong” or “SometimesWrong.” What is clear is that both men and women seem to be on either extremesaying that homosexual relations are “Always Wrong” or “Not Wrong at All.”c.The following frequency distributions contain information on attitudes towardspremarital sex for men and women:Men:Women:

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 21 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionIt is clear from the tables above that the majority of men view premarital sex as “NotWrong at All” (58.6%). Women seem to be more evenly split: 27.0 percent of womenview premarital sex as “Always Wrong” and 45.4 percent view premarital sex as “NotWrong at All.” Also of interest is the category “Almost Always Wrong.” Only asmall percentage of men and women fall into this category. Like attitudes onhomosexual relations, it seems to some degree that men and women are prone towardthe extreme response categories of “Always Wrong” and “Not Wrong at All.”

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 22 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition2.a.The following frequency distributions have been adapted from the SPSS outputs andcontaininformation on the educational levels of men and women:For the most part, both distributions appear symmetrical; the mean, median, andmode for each group are very close. The mean number of years of education for menis 13.67. The mean number of years of education for women is 13.31. The medianfor men is 13, while the median for women is also 13. The modes for men andwomen are identical (12). The slight difference in mean number of years ofeducation between men and women indicates that there are a small number of men

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 23 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionwho have a very high number of years of education; these individualspullthe meanupwards.b.Practically speaking, the difference between male and female educational attainmentis not that great and of little importance. This was not true in the past. Of course,years of education are a crude measure, and the type of school attended probably hasan important effect on type of job and salary. Also, education is only one of thedeterminants of occupation and salary, which is why females can have educationallevels close to males but still be making much less in salary.3.a.Theoretically, there is really no one best measure of central tendency. It is helpful toknow the most common category, the mode, but also the mean and the median, sincethe distributions are not that highly skewed. The best measure is probably the mean,but since number of children (CHILDS) only comes in discrete values, the median isalso valuable. For these particular distributions, the mean is definitely better, becausethe median makes it seem as if all three groups have the same number of children.b.On average, upper class respondents have slightly more children per respondents(mean = 2.23, median = 2.0, mode = 2.0). The median (2.0) is the same for all classes.Working class and lower class have modes of zero, while middle class and upperclass have modes of 2.00.c.With the exception of working class respondents (median = 2.5 kids), the median isthe same for all groups (2 kids). Additionally, all classes had the same mode of 2.0.The mean for lower class respondents (3.55) is the highest of all groups.Lower ClassWorking ClassMiddle ClassUpper ClassMean3.553.093.193.30Median3.02.52.02.0Mode2.02.02.02.0

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 24 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Edition4.a.TVHOURS: mode (2.0), median (2.0), Mean (3.01)b.POLVIEWS: mode (moderate), median (moderate)c.HRS1: mode (40.00), median (40.00), mean (40.62)d.OWNGUN: Mode (no), median (no)e.SIBS: mode (2.0), median (3.0), mean (3.68)f.GRASS: mode (not legal), median (not legal)5.a.The frequency distribution, as well as statistics, for males that are pretty happy isshown below:b.Males with “very happy” (2.84 hours) and “not too happy” (3.17 hours) marriagesreport watching more hours of TV than do males with “pretty happy” marriages (2.55hours). For females, rates of hour spent watching TV have an inverse relationship

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 25 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionwith marital satisfaction. In other words, as marital satisfaction increases, hours spentwatching TV decreases.CHAPTER3EXERCISE SOLUTIONS1.a.The mode can be found two ways: looking for either the highest frequency (470) orthe highest percentage (48.3).The mode is the category that corresponds to thesevalues, “Exciting.”b.The median can be found two ways: by using either the frequencies columnof thecumulative percentages.Using FrequenciesUsing Cumulative PercentagesN+12=974+12=487.5th caseNotice that48.3% of the observations fall inthe “Exciting” percentagecategory;93.9%fall inor belowthe “Routine” category.Starting with the frequency in the first category(470), add up the frequencies until you findwhere the487thand 488thcases fall.Both ofthese cases correspond to the category“Routine,” which is the median.The 50% mark, or the median, is locatedsomewhere within the “Routine” category.So the median is “Routine.”c.The mode is simply the category with the highest frequency (or percentage) in thedistribution. The median divides the distribution into two equal parts so that half thecases are below it and half above it.d.Because thisvariable is an ordinal-level variable.2.a.Ordinal. The mode can be found two ways, either by looking for the highestfrequency (467) or the highest percent (50.2%). The mode is the category thatcorresponds to these values, “Always Wrong.”

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 26 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionb.The median can be found two ways: by using either the frequencies column of thecumulative percentages.Using FrequenciesUsing Cumulative PercentagesN+12=930+12=465.5th caseNotice that 50.2% of the observations fall inthe “Almost alwayswrong” cumulativepercentage category.Starting with the frequency in the first category(472), add up the frequencies until you findwhere the 465thand 466thcases fall. Both ofthese cases correspond to the category“Almost always wrong,” which is themedian.The 50% mark, or the median, is locatedsomewhere within the “Always almostwrong” category. So the median is “Alwaysalmost wrong.”A slight majority of people (50.2%) view homosexual relations as “Always wrong” or“Almost always wrong.” At the other extreme, 37.2% of people view homosexualrelations as “Not wrong at all.”3.a.Interval-ratio. The mode can be found two ways: by looking either for the highestfrequency (14) or the highest percentage (43.8%). The mode is the category thatcorresponds to the value “40 hours worked last week.” The median can be found twoways: by using either the frequencies column or the cumulative percentages.Using FrequenciesUsing Cumulative PercentagesN+12=32+12=16.5th caseNotice that34.4% of the observations fall inorbelowthe “32hours worked last week”category;78.1% fall inor belowthe “40hours worked last week”category.Starting with the frequency in the first category(1), add up the frequencies until you findwhere the16thand 17thcasesfall.Both ofthese casescorrespondto the category “40hours worked last week,” which is themedian.The 50% mark, or the median, is locatedsomewhere within the “40 hours worked lastweek” category. So the median is “40 hoursworked last week.”

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 27 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionb.Since the median is merely a synonym for the 50thpercentile, we already know thatits value is40 hours worked last week.25thpercentile = (32× 0.25) = 8thcase =30hours worked last week75thpercentile = (32 × 0.75) = 24thcase = 40hours worked last week4.a.The median can befound two ways, either by using the frequencies column or byusing the cumulative percentages. However, since the problem only gives thefrequencies, we’ll use those to solve for the median.Using Frequencies𝑁+12=480+12=240.5thcaseStarting with the frequency in the first category (94), add up the frequencies until you find where the 240thand 241stcases fall. Both cases correspond to the category “Somewhat disagree,” which is the median.b.20thpercentile = (480 × 0.20) = 96thcase = “Somewhat agree”80thpercentile = (480 × 0.80) = 384thcase = “Somewhat disagree”5.a.The mode can be found by looking for the highest frequency in each column; themode for each group is listed below:18-29: Good30-39: Good40-49: Good50-59: GoodThe median can be found two ways:by using either the frequencies column or thecumulative percentages.However, since the problem only gives the frequencies, we’lluse those to solve for the median.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 28 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionAge Group18–2930–3940–4950–59N+12=164+12=82.5th caseN+12=169+12=85th caseN+12=168+12=84.5th caseN+12=173+12=86.5th caseStarting with thefrequency in thefirst category (56),add up thefrequencies untilyou find where the82ndand 83rdcasesfall.Bothcasescorrespondto“Good,” which isthe median.Starting with thefrequency in thefirst category (55),add up thefrequencies untilyou find where the85thcasefalls.Thiscasecorrespondsto“Good,” which isthe median.Starting with thefrequency in thefirst category (41),add up thefrequencies untilyou find where the84thand 85thcasesfall. Both casescorrespondto“Good,” which isthe median.Starting with thefrequency in thefirst category (38),add up thefrequencies untilyou find where the86thand 87thcasesfall.Both of thesecases correspondto“Good,” which isthe median.b.Sincethe mode and median for all four age groups was “Good,” it has to do with howrespondents interpreted the question. For instance, it is possible that one’s healthstatus was assessed relative to his or her age. Neither the median nor the modeprovides a better description of the data since they provide the same information.6.a.We begin by summing each of the columns.State20052009Alabama740828Delaware125145Florida3,0083,289Illinois1,6741,806Minnesota691767NewHampshire185217New York2,7582,937Washington807938Σ = 9,988Σ = 10,927Now we divide each sum by 8 (the total number of states). The mean in 2005 is1,248.5 or 9,988/8. We divide by 8 because only 8 states are included in the table.The mean in 2009 is 1,365.9 or 10,927/8.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 29 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionSince the mean is higher in 2009, one could say that on average there are moreAmericans on Medicare in 2009 than in 2005. However, the mean is not the bestmeasure of central tendency because three of the states (Florida, New York, andIllinois) have exponentially more cases than the other states, pulling the mean towarda higher value. You can verify this by computing the median for each year.b.We begin by summing each of the columns after having removed Florida, Illinois,and New York.State20052009Alabama740828Delaware125145Minnesota691767New Hampshire185217Washington807938Σ = 2,548Σ = 2,895The recalculated 2005 mean is 509.6; the mean for 2009 is 579. The mean nowappears to be a more accurate measure of central tendency. Both means are bettermeasures of central tendency now since they are closer to the values for most states.7.We begin by multiplying each household size by its frequency.Household SizeFrequencyFrequency x Y (fY)138138125261,052322768142008005964806422527191338540921810220TotalN= 1,500∑fy= 3,857

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 30 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second EditionY ̅=∑fyN=3,8571,500=2.57So, the mean number of people per household is2.57.8.a.Students might become confused here and try to somehow relate the mode or medianto the names of the states, which are simply labels for the cases. For the 2005 data,there is nomode. Since there are 8 cases, the median is the average of the 4thand 5thcases. Cases must be ordered, from low to high, so the median is (740 +807)/2=773.5. Since the median (773.5) is lower than the mean (1,248.5) for 2005,the distributions are skewed in a positive direction.For the 2009 data, there is no mode. Since there are 8 cases, the median is the averageof the 4th and 5th cases. Cases must be ordered, from low to high, so the median is(828 + 938)/2=883. Since the median (883) is lower than the mean (1,365.9) for2009, the distributions are skewed in a positive direction.b.Because of the very high values of Medicare enrollees for Illinois, New York, andFlorida, the mean is inflated and does not accurately portray the number of enrolleesin each state. Therefore, the median is a better estimation of 2005 and 2009 Medicareenrollees.c.As mentioned before, the extreme number of Medicare enrollees for Florida, Illinois,and New York “pulls” the mean upward, thereby creating a positively skeweddistribution.9.a.There appear to be a few outliers (i.e., extremely high values); this leads us tobelieve that the distribution is skewed in the positive direction.

Essentials of Social Statistics for a Diverse Society Second Edition Solution Manual - Page 31 preview image

Loading page ...

Frankfort-Nachmias and Leon-Guerrero:Social Statistics for a Diverse Society,Essentials Second Editionb.The median can be foundtwo ways: by using either the frequencies column or thecumulative percentages. The data are in frequencies; we’ll use those to solve themedian. Since the median(2) is less than the mean (2.57), we can conclude that thedistribution is skewed in a positive direction. Our answer to question 9a is furthersupported.Using FrequenciesN+12=1,500+12=750.5th caseStarting with the frequency in the first category (381), add up the frequencies until you findwhere the750thand 751stcases fall. Both of these cases correspond to the category “2,” whichis the median.10.a.We begin by multiplying each category by its frequency.

Preview Mode

This document has 137 pages. Sign in to access the full document!

Report

Study Now!

Document Details

Related Documents

Essentials of Social Statistics for a Diverse Society Second Edition Test Bank

Statistics - Univariate Inferential Tests

Statistics - Sampling

Statistics - Probability

Statistics - Principles of Testing

Statistics - Numerical Measures

Statistics - Introduction to Statistics

Statistics - Graphic Displays

Statistics - Cummulative Reviews

Statistics - Common Mistakes and Tables

Company

Explore

Study Tools