Please solve math problems:-
SW: As the head of a social services agency, you believe your staff of 20 social workers is very much overworked compared to 10 years ago. The caseloads for each worker are reported for each of the two years in question. Has the average caseload increased? What measure of central tendency is most appropriate to answer this question? Why? 2000 2010 52 55 42 82 50 40 75 50 67 52 49 162 45 55 85 65 189 68 42 50 50 42SW: For the test scores first presented in problem 2.6 and reproduced here, compute a median and mean for the pretest and posttest and then interpret these statistics. Problem 2.8: SW: A local youth service agency has begun a sex education program for teenage girls who have been referred by the juvenile courts. The girls were given a 20-item test for general knowledge about sex, contraception, and anatomy and physiology on admission to the program and again after completing the program. The scores of the first 15 girls to complete the program are: Protest Postical 12 13 10 12 15 19 17 12 11 7 12 20 5 10 15 11 12 20 Construct frequency distributions for the pretest and posttest scores. Include a column for percentages. (HINT: There were 20 items on the test, so the maximum range for these scores is 20. If you use 10 class intervals to display these scores, the interval size will be 2. Because there are no scores of 0 or 1 for either test, you may state the first interval as 2-3. To make comparisons easier, both frequency distributions should have the same intervals.)SOC; A sample of 25 freshmen at a major university completed a survey that measured their degree of racial prejudice (the higher the score, the greater the prejudice). 3. Compute the median and mean scores for these data 10 43 30 30 45 40 12 40 42 35 TO 42 32 39 11 AT 27 37 10 b. These same 25 students completed the same survey during their senior year. Compute the median and mean for this second set of scores and then compare them to the earlier set. What happened? 10 45 35 27 50 10 50 40 37 10 15 30 20 43 25 30 40 10You have compiled the following information on each of the graduates voted "most likely to succeed" by a local high school for a 10-year period. For each variable, find the appropriate measure of central tendency. Present Young of Education Case Income ($) Marital Status Owns a Home? Post-High School 104 0DO Divorced Yes 681000 Divorced No 54 000 Married A 45.000 Married No Single No Separated Yes 301000 Married No 27/00O Married No 231000 Married SingleProfessional athletes are threatening to strike because they claim that they are underpaid. The team owners have released a statement that says. in part. "The average salary for players was $1.2 million last year." The players counter by issuing their own statement that says, in part, "The typical player earned only $753,000 last year." Is either side necessarily lying? If you were a sports reporter and had just read Chapter 3 of this text, what questions would you ask about these statistics?In this exercise, you will use SPSS to get measures of central tendency for several different variables in the States data set, which is available from the Web site for this text. . Find and click the SPSS icon on your desktop. . Load the States data set. . From the menu bar across the top of the SPSS window. click Analyze, Descriptive Statistics, and Frequencies. . Find these variables in the box on the left of the Frequencies window: FamPoor09 (percentage of all families in the state below the poverty line), ForBorn (percentage of the population in the state that was born outside the United States in 2009), and TeenBirths (percentage of all births in the state that were to mothers younger than 20). Click the arrow to move the variable names into the box on the right. . Click the Statistics button and, under "Central Tendency," select Mean, Median, and Mode. Click Continue to return to the Frequencies window. . Make sure the box next to the "Display frequency tables" option is not checked. We are interested only in the summary statistics, not in the tables. . Click OK. a. Write a paragraph analyzing and summarizing the three variables. Are any of the distributions skewed? In what direction? b. Select one of the skewed variables and skim the scores of the variable in the SPSS Data Editor to find the outlier(s). That is, find the column in which the scores of the variable are stored and skim the scores looking for especially high scores (if the skew is positive) or low scores (if the skew is negative). What sociological factors might account for these very high or low scores?Compute the range and standard deviation of the following 10 scores. (HINT: It will be helpful to organize your computations as in Table 4.4.) 10, 12. 15, 20, 25, 30, 32, 35, 40, 50 Table 4.4: TABLE 4.4 Computing the Standard Deviation for Two Campuses Residential Campus Scores (X) Deviations (X - X) Deviations Squared (X - X) 18 [18 - 19) - -1 (-17 - 1 18 (18 - 18) = 0 1OF =0 20 (20 - 19) - 1 (1) - 1 18 (18 - 10) - -1 (-17 - 1 20 (20 - 19) = 1 (1) = 1 EX - 95 EX - X)= 0 SIX -XY =4 EX X = 05 N 5 Urban Campus Sooren (X;] Deviations (X - I) Deviations Squared (X -X] 20 (20 - 23) - -3 (-ap - 9 22 (22 - 23) - -1 (-17 - 1 10 (10 - 21) = -5 1-67 = 25 35 (25 - 23) - 2 (27 - 4 (0 - 20) = 7 (7) = 49 E(X) - 115 EX - D = XOX - XY =0 115 N 23SW: Compute the standard deviation for the pretest and posttest scores that were used in problem 3.12. The scores are reproduced here. Taking into account all of the information you have on these variables, write a paragraph describing how the sample changed from test to test. What does the standard deviation add to the information you already had? Case Pretest Posttest 12 7 13 10 12 15 10 8 10 17 3 12 10 11 5 T 12 20 5 10 15 11 12Labor force participation rates (percent employed), percent high school graduates, and mean income for males and females in 10 states are reported here. Calculate the mean and the standard deviation for both groups for each variable and describe the differences. Are males and females unequal on any of these variables? How great is the gender inequality? Labor Force Participation Rate Percentage HS Graduates Mean Income State Foralo Female 65.B 54.3 D 76.T DE9 52 345 S 71.8 56 789 76.1 80 5 48.007 75.1 83.1 88.7 621023 80.9 81.1 86 3 38.4 55.000 73.6 47-1 49.145 70.5 04.1 61 210 74.L 67.1 91.GData on several variables measuring overall health and well-being for eleven nations are reported here for 2010. with projections to 2020. Are nations becoming more or less diverse on these variables? Calculate the mean, range, and standard deviation for each year for each variable. Summarize the results in a paragraph. Life Expectancy (years) Inlant Mortality Rate" Fertility Rate Nation 2010 2020 2010 2020 27101 Canada 5.0 4.4 China 75 70 16.5 12.6 1.5 Egypt 75 26.2 179 DE Germany 4.0 1.4 Japan 83 2.7 12 Mali 52 113.7 91.9 6.6 Mexico 76 78 17.8 13.2 23 71 74 27.7 202 23 Ukraine 70 8.7 73 13 U.S. 80 B.1 5.4 2.1 Zambia 52 54 88.4 5018 "Number of deaths of children under one year of age per 1000 live births. "Average number of chikiron per female Source. L.8. Bureau of the Census, 2012. Stanstical Abstract of the United States 2012. p. 842.\fYou are 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 here. Which department will win the award? Why? Departments A A C D X - 601.30 693 17 507 70 2732 40.17At St. Algebra College, the math department ran some special sections of the freshman math course by using a variety of innovative teaching techniques. Students were randomly assigned to either the traditional sections or the experimental sections, and all students were given the same final exam. The results of the final are summarized here. What was the effect of the experimental course? Traditional Experimental X - 77.8 X - 76.8 8 = 12.1 8=02 N - 478 N - 465SOC: Compute the standard deviation for both sets of data presented in problem 3.13 and reproduced here. Compare the standard deviation computed for freshmen with the standard deviation computed for seniors. What happened? Why? Does this change relate at all to what happened to the mean over the four-year period? How? What happened to the shapes of the underlying distributions? Freshmen 43 45 40 12 40 12 35 45 10 33 42 38 11 47 22 37 10 Seniors 10 15 35 27 50 10 40 0 40 10 10 10 15 30 20 43 2L 40In this exercise, you will once again use the States data set, this time to analyze changes in the level of poverty between 2000 and 2000. We will use the Descriptives command to generate output. . Find and click the SPSS icon on your desktop. . Load the States data set. . From the menu bar across the top of the SPSS window. click Analyze, Descriptive Statistics, and Descriptives. . In the list of variables, find FamPoor00 (the percentage of families below the poverty line in each state in 2000) and FamPoor09 (the percentage of families below the poverty line in 2009). Click the arrow to move the variable names into the box on the right. . Click the Options tab and check the box to select the Range. Click Continue and then click OK . OPTIONAL: To get boxplots for these variables: . Click Graphs, Legacy Dialogs, and Boxplot. . On the Boxplot window, check "Summaries of separate variables" and then click Define . Find Fampoor00 and Fampoor09 in the list of variables, and click the arrow to move the variable names into the "Boxes Represent" box. . Click OK. Write a paragraph describing the changes in family poverty between 2000 and 2009. Be sure to discuss central tendency and dispersion separately, and clearly identify each statistic. (OPTIONAL: Include an analysis of the boxplots.) It may be helpful to model your paragraph on one of the discussions presented earlier in this chapter
