Chapter Questions
Compute the range and standard deviation of the following 10 scores. (HINT: It will be helpful to organize your computations as in Table 4.3.)$$10,12,15,20,25,30,32,35,40,50$$
Compute the range and standard deviation of the following 10 test scores.$$77,83,69,72,85,90,95,75,55,45$$
In problem $3.1$ at the end of Chapter 3 , you calculated measures of central tendency for six variables for freshman and seniors. Three of those variables are reproduced here. Calculate the mean (if necessary), the range, and the standard deviation for each variable. What information is added by the measures of dispersion? Write a paragraph summarizing the differences between freshmen and seniors.
SOC In problem $3.5$ at the end of Chapter 3 , you calculated measures of central tendency for four variables for 15 respondents. Two of those variables are reproduced here. Calculate the mean (if necessary), the range, and the standard deviation for each variable. What information is added by the measures of dispersion?
SOC In problem $3.8$, you computed mean and median income for 13 Canadian provinces and territories in two separate years. Now compute the standard deviation and range for each year, and taking account of the two measures of central tendency and the two measures of dispersion, write a paragraph summarizing the distributions. What do the measures of dispersion add to what you already knew about central tendency? Did the provinces become more or less variable over the period? The scores are reproduced here.
SOC Data on several variables measuring overall heath and well-being for five nations are reported here for 2005 , 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.
SOC Labor force participation rates (percent employed), percent high school graduates, and mean income for males and females in 10 states are reported here. Calculate a mean and a standard deviation for both groups for each variable and then describe the differences. Are males and females unequal on any of these variables? How great is the gender inequality?
SW 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?
SOC In problem 3.11, you computed measures of central tendency for the price of a liter of regular gas for 20 nations. The scores are reproduced here. Compute the standard deviation for this variable and then write a paragraph summarizing the mean, median, and standard deviation.
CJ/SW Per capita expenditures for police protection for 20 cities are reported here for 2000 and $2010 .$ Compute a mean and standard deviation for each year and then describe the differences in expenditures for the five-year period.
SOC Compute the range and standard deviation for the data presented in problem $3.14 .$ The data are reproduced here. What would happen to the value of the standard deviation if you removed Los Angeles from this distribution and recalculated? Why?
SOC Listed here are the rates of abortion per 100,000 women for 20 states in 1973 and 1975 . Describe what happened to these distributions over the two-year period. Did the average rate increase or decrease? What happened to the dispersion of this distribution? What happened between 1973 and 1975 that might explain these changes in central tendency and dispersion? (Hint: It was a Supreme Court decision.)
SW One of your goals as the new chief administrator of a large social service bureau is to equalize workloads within the various divisions of the agency. You have gathered data on caseloads per worker within each division. Which division comes closest to the ideal of an equalized workload? Which is farthest away?
SOC 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?
\begin{tabular}{|l|l} \hline SOC/CJ & Calculate the range and standard devia- \end{tabular} tion for the homicide rates presented in problem 3.15 and reproduced here. Using all the information you have on central tendency and dispersion, write a paragraph describing the changes in this variable between 1994 and $2009 .$
At 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?
You 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?