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

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    Frankfort - Nachmias and Leon - Guerrero: Social Statisti cs for a Diverse Society, Essentials Second Edition Chapter 1 – Answers to All Exercises 1. Once our research question, the hypothesis, and the study variables have been selected, we move on to the next stage of the research process – measuring and collecting the data. The choice of a particular data collection method or instrument depends to our study objective. After our data have been collected, we have to find a systematic way to organize and analyze our data and set up some set of procedures 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 but less 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 persons than those not married. e. As military expenditures as a percentage of GNP increase, the overall level of security may decrease, as witnessed by many Third World countries, or in the troubled Middle East. In fact, military expenditures (except during the Cold War) often increase because of rising conflict, but those 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 ratio b. Nominal c. Interval ratio d. Ordinal e. Nominal f. Interval ratio g. Interval ratio h. Nominal 4. a. Discrete c. Continuous f. Discrete g. Continuous 5. There are many possible variables from which to choose. Some of the most common selections by students will probably be: type of occupation or industry, work experience, and educational training or expertise. Students should first address the relationship between these variables and gender. For example, Men have more years of work experience than women in the same occupation. Student may also consider measuring structural bias or discrimination. 6. a. Unemployment records could be used to determine the actual number of unemployed; a descriptive 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 all Asian women, so this would be a descriptive statistic. d. The ratings will be gathered from a survey, so this is inferential.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statisti cs for a Diverse Society, Essentials Second Edition e. A university should be able to report GPA by major, so this is a descriptive statistic based upon the population. f. In theory, the U.S. records accurately all immigrants to this country. Therefore, the number of South East Asian immigrants would be a descriptive statistic. However , because of illegal immigration, surveys are also taken to estimate the total number of legal and unauthorized immigrants . 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 reported first. It is estimated that the majority of crimes are not reported to authorities. Data on reported crimes 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 in the 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 party membership, like this: Behavior Code Didn’t vote, no membership 0 Voted, no membership OR Membership, didn’t vote 1 Voted and membership 2 These codes are ordinal in scale because the amount of political participation can be ranked from high to low. Other possible ordinal variables can be constructed from other sets of behaviors, such as working in a candidate’s campaign, signing a petition, and so forth. The key points are to create a variable 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 in which a person has voted since becoming eligible to vote, or the amount of money a person donated 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 years reported. As discussed in the chapter, interval ratio variables are the highest level of measurement and can also be measured at ordinal or nominal levels. Annual income: This variable could be measured as an interval - ratio variable, with actual dollar earnings reported. Religiosity: This variable could be measured in several ways. For example, as church attendance, the variable 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 S olutions NA

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

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition Chapter 2 – Answers to Exercises (in - text) 1. a. Race is a nominal variable. Class is an ordinal variable, since the categories can be ordered from lower to higher status. b. Frequency Table for Race Race Frequency (f) White 17 Nonwhite 13 Total (N) 30 Frequency Table for Class Class Frequency (f) Lower 3 Working 15 Middle 11 Upper 1 Total (N) 30 2. Class Percentage Lower 10.0% Working 50.0% Middle 36.7% Upper 3.3% Total 100% a. The smallest perceived class is the upper class, composing only 3.3% of the survey. b. Together, the working and middle class compose 86.7% of the survey. 3. Number of traumas Frequency (f) 0 15 1 11 2 4 Total (N) 30 Trauma 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.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition White 57% Nonwhite 43% Lower 10% Working 50% Middle 37% Upper 3%

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition 5. Ranking them from highest to lowest level of support: Strong Democrats, Strong Republicans and Independents. Support does vary by group, however, the majority of strong Democrats (56.8%) and strong Republicans (50%) agree/strongly agree with the statement. The group with the lowest level of support is Independents with 42.3%. 6. Email hours per week Frequency Cf % C% 0 19 19 19 19 1 20 39 20 39 2 13 52 13 52 3 5 57 5 57 4 2 59 2 59 5 6 65 6 65 6 5 70 5 70 7 2 72 2 72 8 3 75 3 75 9 1 76 1 76 10 or more 23 99 23 99 Total 99 99% b. .575 (57/99) spent 3 hours or less 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. 0 2 4 6 8 10 12 14 16 0 1 2

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition 7. a. For whites. Education f % C% Less than high school 72 12.3 12.3 High school graduate 272 46.5 58.8 Junior college 46 7.9 66.7 Bachelor 118 20.2 86.9 Graduate 77 13.2 100.1 TOTAL 585 For blacks. Education f % C% Less than high school 26 22.0 22.0 High school graduate 59 50 72.0 Junior college 10 8.5 80.5 Bachelor 16 13.6 94.1 Graduate 7 5.9 100.0 TOTAL 118 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition For males. Education f % C% Less than high school 46 14.0 14.0 High school graduate 151 45.9 59.9 Junior college 24 7.3 67.2 Bachelor 65 19.8 87 Graduate 43 13.1 100.1 TOTAL 329 For females. Education f % C% Less than high school 67 15.0 15.0 High school graduate 214 47.8 62.8 Junior college 37 8.2 71.0 Bachelor 81 18.1 89.1 Graduate 49 10.9 100.0 TOTAL 448 b. 40.2 % of males attended school beyond high school. A lower percentage of females (37.2%) did the same. 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. Inequality appears to be larger between racial groups. A larger percentage of whites complete bachelor or graduate degrees 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 West geographic regions. b. Pie charts can be used to compare the demographic data. However, age and percent of poverty level are 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. Blacks are 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 than Asians through 2012. Hispanics and Asians have the lowest voting rates for all groups. As noted in 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% from 2008 to 2012. The highest voting rate for whites was in 2004 (67.2%), 2008 for Hispanics (49.9%) and for Asians (47.6%).

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition 10. b. The shapes of both histograms are similar, which indicates that both groups have roughly the same 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. Whites have higher educational attainment, 15.4% of whites vs. 9.3% of blacks completed 17 - 20 years of education. 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, all rates are below 5 per 1,000 females. Across the three time periods, victimization rates are highest for females age 12 - 17 (11.3 to 4.1). Second highest rates are among females age 18 - 34 year (7.0 to 3.7). 12. For sex and age: Women were more likely than men to indicate that same - sex marriage should be legal. There was an increase in both age groups for men and women. The highest increase was among men ages 18 - 49 years. For age: There is an increase in support across all three age groups. The largest increase was among those 18 - 34 years of age (70 - 54 = 16%). For political affiliation: There was an increase in the percent 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 marriage among 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 for the 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 strongly agree or agree to the statement. Based on these responses, women are more likely to be worried about receiving second - class health care than men. 0 5 10 15 20 25 30 35 40 45 0-4 5-8 9-12 13-16 17-20 Whites Blacks

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition Chapter 2 SPSS Solutions 1. 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, and never married: 8.9 + 15.8 + 24.6 = 49.3% 2.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition b. Each variable is an ordinal measurement. [Review the definitions of levels of measurement.] The higher value (5) indicates strong disagreement to the statement. Overall, respondents express positive 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 immigrants take 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 of family generations in the household (FAMGEN). 4. Students are encouraged to determine on their own how to recode the variable. Students should consider how the years of education is related to degree attainment, for example: 12 years = high school graduate 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 no countries where the male labor force participation rate was 50% or less. Out of the 70 countries, all the

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

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

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition c. Overall, almost two third of the respondents are above 45. The largest age category for both male and female respondents is the oldest group, 45+. A slightly higher percent of males are 45 or older (74.91%) than the females (65.7%). The second largest age group is the youngest one, 18 - 34. 17.38% of the female respondents fall in this category as compared to their male counterparts of whom 12.37% are between 18 to 34 years of age. 7 . The amount of respondents who have ever looked for information about health or medical topics from any source increases as educational degree increases, from 44.4% among those with less than 8 years of education to 93.1% among those with a postgraduate degree. You can see the increase in this category by tracking 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, very good and good health. A slightly higher percentage of males report fair health (13.1 vs. 11.9%) than women and slightly more women report poor health (3.4 vs. 2.9%) than women.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition b. 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 the female respondents fall as compared to only 0.178% of their male counterparts.

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

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition 9 . RentOrOwn : nominal WhenDiagnosedCancer : interval IncomeRanges - ordinal QualityCare : ordinal Interval data is best displayed in histograms, while ordinal and nominal data can be displayed in pie charts or bar graphs.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition CHAPTER 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 measured at the ordinal level. Therefore, the median is the appropriate measure of central tendency 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 towards homosexual relations for men and women: Men: Women:

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition From the tables above, it appears that men and women have pretty similar attitudes on homosexual relations. That is, 51.7 percent of men and 49.2 percent of women say that homosexual relations are “Always Wrong.” Additionally, 35.4 percent of men and 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 middle saying that homosexual relations are either “Almost Always Wrong” or “Sometimes Wrong.” What is clear is that both men and women seem to be on either extreme saying that homosexual relations are “Always Wrong” or “Not Wrong at All.” c. The following frequency distributions contain information on attitudes towards premarital sex for men and women: Men: Women:

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

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition 2. a. The following frequency distributions have been adapted from the SPSS outputs and contain information on the educational levels of men and women: For the most part, both distributions appear symmetrical; the mean, median, and mode for each group are very close. The mean number of years of education for men is 13.67. The mean number of years of education for women is 13.31. The median for men is 13, while the median for women is also 13. The modes for men and women are identical (12). The slight difference in mean number of years of education between men and women indicates that there are a small number of men

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition who have a very high number of years of education; these individuals pull the mean upwards. b. Practically speaking, the difference between male and female educational attainment is 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 has an important effect on type of job and salary. Also, education is only one of the determinants of occupation and salary, which is why females can have educational levels 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 to know the most common category, the mode, but also the mean and the median , since the 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 is also valuable. For these particular distributions, the mean is definitely better, because the 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 upper class have modes of 2.00. c. With the exception of working class respondents (median = 2.5 kids), the median is the 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 Class Working Class Middle Class Upper Class Mean 3.55 3.09 3.19 3.30 Median 3.0 2.5 2.0 2.0 Mode 2.0 2.0 2.0 2.0

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition 4. 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 is shown below: b. Males with “very happy” (2.84 hours) and “not too happy” (3.17 hours) marriages report watching more hours of TV than do males with “pretty happy” marriages (2.55 hours). For females, rates of hour spent watching TV have an inverse relationship

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition with marital satisfaction. In other words, as marital satisfaction increases, hours spent watching TV decreases. CHAPTER 3 EXERCISE SOLUTIONS 1. a. The mode can be found two ways: looking for either the highest frequency ( 470 ) or the highest percentage ( 48.3 ). The mode is the category that corresponds to these values, “Exciting.” b. The median can be found two ways: by using either the frequencies column of the cumulative percentages. Using Frequencies Using Cumulative Percentages N + 1 2 = 974 + 1 2 = 487.5th case Notice that 48.3 % of the observations fall in the “ Exciting” percentage category; 93.9 % fall in or below the “Routine” category. Starting with the frequency in the first category (4 70 ), add up the frequencies until you find where the 487 th and 488 th cases fall . Both of these cases correspond to the category “Routine,” which is the median. The 50% mark, or the median, is located somewhere within the “ Routine ” cate gory. So the median is “Routine .” c. The mode is simply the category with the highest frequency (or percentage) in the distribution. The median divides the distribution into two equal parts so that half the cases are below it and half above it. d. Because this variable is an ordinal - level variable. 2. a. Ordinal. The mode can be found two ways, either by looking for the highest frequency (467) or the highest percent (50.2%). The mode is the category that corresponds to these values, “Always Wrong.”

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition b. The median can be found two ways: by using either the frequencies column of the cumulative percentages. Using Frequencies Using Cumulative Percentages N + 1 2 = 930 + 1 2 = 465.5th case Notice that 50.2% of the observations fall in the “Almost always wrong” cumulative percentage category. Starting with the frequency in the first category (472), add up the frequencies until you find where the 465 th and 466 th cases fall. Both of these cases correspond to the category “Almost always wrong,” which is the median. The 50% mark, or the median, is located somewhere within the “Always almost wrong” category. So the median is “Always almost 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 homosexual relations as “Not wrong at all.” 3. a. Interval - ratio. The mode can be found two ways: by looking either for the highest frequency (14) or the highest percentage (43.8%). The mode is the category that corresponds to the value “40 hours worked last week.” The median can be found two ways: by using either the frequencies column or the cumulative percentages. Using Frequencies Using Cumulative Percentages N + 1 2 = 32 + 1 2 = 16.5th case Notice that 34.4 % of the observations fall in or below the “3 2 hours worked last week” category; 78.1 % fall in or below the “ 40 hours worked last week ” category. Starting with the freq uency in the first category (1 ), add up the frequencies until you find where the 16 th and 17 th case s fall. Both of these cases correspond to the category “40 hours worked last week,” which is the median. The 50% mark, or the median, is located somewhere within the “ 40 hours worked last week ” category. So the median is “ 40 hours worked last week .”

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition b. Since the median is merely a synonym for the 50 th percentile, we already know that its value is 40 hours worked last week. 25 th percentile = (32 × 0.25) = 8 th case = 30 hours worked last week 75 th percentile = (32 × 0.75) = 24 th case = 40 hours worked last week 4. a. The median can be found two ways, either by using the frequencies column or by using the cumulative percentages. However, since the problem only gives the frequencies, we’ll use those to solve for the median. Using Frequencies 𝑁 + 1 2 = 480 + 1 2 = 240 . 5th case Starting with the frequency in the first category (94), add up the frequencies until you find where the 240 th and 241 st cases fall. Both cases correspond to the category “Somewhat disagree,” which is the median. b. 20 th percentile = (480 × 0.20) = 96 th case = “Somewhat agree” 80 th percentile = (480 × 0.80) = 384 th case = “Somewhat disagree” 5. a. The mode can be found by looking for the highest frequency in each column; the mode for each group is listed below: 18 - 29: Good 30 - 39: Good 40 - 49: Good 50 - 59: Good The med ian can be found two ways: by using either the frequencies column or the cumulative percentages. However, since the problem only gives the frequencies, we’ll use those to solve for the median.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition Age Group 18 – 29 30 – 39 40 – 49 50 – 59 N + 1 2 = 164 + 1 2 = 82.5th case N + 1 2 = 169 + 1 2 = 85th case N + 1 2 = 168 + 1 2 = 84.5th case N + 1 2 = 173 + 1 2 = 86.5th case Starting with the frequency in the first category ( 56 ), add up the frequencies until you find where the 82 nd and 83 rd case s fall . Both case s correspond to “Good,” which is the median. Starting with the frequency in the first category ( 55 ), add up the frequencies until you find where the 85 th case fall s . This case c orrespond s to “Good,” which is the median. Starting with the fre quency in the first category (41 ), add up the frequen cies until you find where the 84 th and 85 th case s fall . Both cases correspond to “Good,” which is the median. Starting with the fre quency in the first category (38 ), add up the frequencies until you find where the 86 th and 87 th case s fall. Both of these cases correspond to “Good,” which is the median. b. Since the mode and median for all four age groups was “Good,” it has to do with how respondents interpreted the question. For instance, it is possible that one’s health status was assessed relative to his or her age. Neither the median nor the mode provides a better description of the data since they provide the same information. 6. a. We begin by summing each of the columns. State 2005 2009 Alabama 740 828 Delaware 125 145 Florida 3,008 3,289 Illinois 1,674 1,806 Minnesota 691 767 New Hampshire 185 217 New York 2,758 2,937 Washington 807 938 Σ = 9,988 Σ = 10,927 Now we divide each sum by 8 (the total number of states). The mean in 2005 is 1,248.5 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.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition Since the mean is higher in 2009, one could say that on average there are more Americans on Medicare in 2009 than in 2005. However, the mean is not the best measure of central tendency because three of the states (Florida, New York, and Illinois) have exponentially more cases than the other states, pulling the mean toward a 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. State 2005 2009 Alabama 740 828 Delaware 125 145 Minnesota 691 767 New Hampshire 185 217 Washington 807 938 Σ = 2,548 Σ = 2,895 The recalculated 2005 mean is 509.6; the mean for 2009 is 579. The mean now appears to be a more accurate measure of central tendency. Both means are better measures 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 Size Frequency Frequency x Y (fY) 1 381 381 2 526 1,052 3 227 681 4 200 800 5 96 480 6 42 252 7 19 133 8 5 40 9 2 18 10 2 20 Total N = 1,500 ∑ fy = 3,857

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition Y ̅ = ∑ fy N = 3,857 1,500 = 2.57 So, the mean number of people per household is 2.57 . 8. a. Students might become confused here and try to somehow relate the mode or median to the names of the states, which are simply labels for the cases. For the 2005 data, there is no mode. Since there are 8 cases, the median is the average of the 4 th and 5 th cases. 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 average of 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) for 2009, the distributions are skewed in a positive direction. b. Because of the very high values of Medicare enrollees for Illinois, New York, and Florida, the mean is inflated and does not accurately portray the number of enrollees in each state. Therefore, the median is a better estimation of 2005 and 2009 Medicare enrollees. c. As mentioned before, the extreme number of Medicare enrollees for Florida, Illinois, and New York “pulls” the mean upward, thereby creating a positively skewed distribution. 9. a. There appear to be a few outliers (i.e., extremely high values); this leads us to believe that the distribution is skewed in the positive direction.

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    Frankfort - Nachmias and Leon - Guerrero: Social Statistics for a Diverse Society, Essentials Second Edition b. The median can be found two ways: by using either the frequencies column or the cumulative percentages. The data are in frequencies; we’ll use those to solve the median. Since the median (2) is less than the mean (2.57 ) , we can conclude that the distribution is skewed in a positive direction. Our answer to question 9a is further supported. Using Frequencies N + 1 2 = 1,500 + 1 2 = 750.5th case Starting with the freq uency in the first category (381 ), add up the frequencies until you find where the 75 0 th and 751 st cases fall. Both of these cases correspond to the category “ 2 ,” which is the median. 10. a. We begin by multiplying each category by its frequency.

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