ࡱ>  qspvm1^^ LbjbjcTcT .>>D   UUUiiiii|qMMMM,,,3|5|5|5|5|5|5|$~.Y|U %(, % %Y|  MMn|))) %p MUM3|) %3|))Ju\^{M`r%ki%wB||0|!x(0&({(U{,* l)!$"f,,,Y|Y|',,,| % % % %(,,,,,,,,, : Descriptive Statistics: homework Exercise 1 Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:  EMBED Photoshop.Image.8 \s  Find the sample mean, EMBED Equation  . Find the sample standard deviation, s. Construct a histogram of the data. Complete the columns of the chart. Find the first quartile. Find the median. Find the third quartile. Construct a box plot of the data. What percent of the students saw fewer than three movies? Find the 40th percentile. Find the 90th percentile. Construct a line graph of the data. Construct a stem plot of the data. Exercise 2 The median age for U.S. blacks currently is 30.1 years; for U.S. whites it is 36.6 years. (Source: U.S. Census). Based upon this information, give two reasons why the black median age could be lower than the white median age. Does the lower median age for blacks necessarily mean that blacks die younger than whites? Why or why not? How might it be possible for blacks and whites to die at approximately the same age, but for the median age for whites to be higher? Exercise 3 Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows:  EMBED Photoshop.Image.8 \s  Find the sample mean EMBED Equation  Find the sample standard deviation, ss Construct a histogram of the data. Complete the columns of the chart. Find the first quartile. Find the median. Find the third quartile. Construct a box plot of the data. What percent of the students owned at least five pairs? Find the 40th percentile. Find the 90th percentile. Construct a line graph of the data. Construct a stem plot of the data. Exercise 4 600 adult Americans were asked by telephone poll, What do you think constitutes a middle-class income? The results are below. Also, include left endpoint, but not the right endpoint. (Source: Time magazine; survey by Yankelovich Partners, Inc.) Note: "Not sure" answers were omitted from the results.  EMBED Photoshop.Image.8 \s  What percent of the survey answered "not sure"? What percent think that middle-class is from $25,000 - $50,000 ? Construct a histogram of the data Should all bars have the same width, based on the data? Why or why not? How should the <20,000 and the 100,000+ intervals be handled? Why? Find the 40th and 80th percentiles. Construct a bar graph of the data. Exercise 5 Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year (Source: San Jose Mercury News). 177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265 Organize the data from smallest to largest value. Find the median. Find the first quartile. Find the third quartile. Construct a box plot of the data. The middle 50% of the weights are from _______ to _______. If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why? If our population were the San Francisco 49ers, would the above data be a sample of weights or the population of weights? Why? Assume the population was the San Francisco 49ers. Find: Exercise 6 An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he? Who is the fastest runner with respect to his or her class? Explain why. Exercise 7 In a survey of 20 year olds in China, Germany and America, people were asked the number of foreign countries they had visited in their lifetime. The following box plots display the results.  In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected. Explain how it is possible that more Americans than Germans surveyed have been to over eight foreign countries. Compare the three box plots. What do they imply about the foreign travel of twenty year old residents of the three countries when compared to each other? Exercise 8 Twelve teachers attended a seminar on mathematical problem solving. Their attitudes were measured before and after the seminar. A positive number change attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows: { 3; 8; -1; 2; 0; 5; -3; 1; -1; 6; 5; -2 } What is the average change score? What is the standard deviation for this population? What is the median change score? Find the change score that is 2.2 standard deviations below the mean. Exercise 9 Three students were applying to the same graduate school. They came from schools with different grading systems. Which student had the best G.P.A. when compared to his school? Explain how you determined your answer.  EMBED Photoshop.Image.8 \s  Exercise 10 Given the following box plot:  Which quarter has the smallest spread of data? What is that spread? Which quarter has the largest spread of data? What is that spread? Find the Inter Quartile Range (IQR). Are there more data in the interval 5 - 10 or in the interval 10 - 13? How do you know this? Which interval has the fewest data in it? How do you know this? 0-2 2-4 10-12 12-13 Exercise 11 Given the following box plot:  Think of an example (in words) where the data might fit into the above box plot. In 2-5 sentences, write down the example. What does it mean to have the first and second quartiles so close together, while the second to fourth quartiles are far apart? Exercise 12 Santa Clara County, CA, has approximately 27,873 Japanese-Americans. Their ages are as follows. (Source: West magazine)  EMBED Photoshop.Image.8 \s  Construct a histogram of the Japanese-American community in Santa Clara What percent of the community is under age 35? Which box plot most resembles the information above?  Exercise 13 Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, each asked adult consumers the number of fiction paperbacks they had purchased the previous month. The results are below.  EMBED Photoshop.Image.8 \s  Find the relative frequencies for each survey. Write them in the charts. Using either a graphing calculator, computer, or by hand, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of 1. For Publisher C, make bar widths of 2. In complete sentences, give two reasons why the graphs for Publishers A and B are not identical. Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not? Make new histograms for Publisher A and Publisher B. This time, make bar widths of 2. Now, compare the graph for Publisher C to the new graphs for Publishers A and B. Are the graphs more similar or more different? Explain your answer. Exercise 14 Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis. At the end of the cruise, guests pay one bill that covers all on-board transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Below is a summary of the bills for each group.  EMBED Photoshop.Image.8 \s  Fill in the relative frequency for each group. Construct a histogram for the Singles group. Scale the x-axis by $50. widths. Use relative frequency on the y-axis. Construct a histogram for the Couples group. Scale the x-axis by $50. Use relative frequency on the y-axis. Compare the two graphs: List two similarities between the graphs. List two differences between the graphs. Overall, are the graphs more similar or different? Construct a new graph for the Couples by hand. Since each couple is paying for two individuals, instead of scaling the x-axis by $50, scale it by $100. Use relative frequency on the y-axis. Compare the graph for the Singles with the new graph for the Couples: List two similarities between the graphs. Overall, are the graphs more similar or different? By scaling the Couples graph differently, how did it change the way you compared it to the Singles? Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person in a couple? Explain why in one or two complete sentences. Exercise 15 Refer to the following histograms and box plot. Determine which of the following are true and which are false. Explain your solution to each part in complete sentences.  The medians for all three graphs are the same. We cannot determine if any of the means for the three graphs is different. The standard deviation for (b) is larger than the standard deviation for (a). We cannot determine if any of the third quartiles for the three graphs is different. Exercise 16 Refer to the following box plots.  In complete sentences, explain why each statement is false. Data 1 has more data values above 2 than Data 2 has above 2. The data sets cannot have the same mode. For Data 1, there are more data values below 4 than there are above 4. For which group, Data 1 or Data 2, is the value of 7 more likely to be an outlier? Explain why in complete sentences Exercise 17 In a recent issue of the IEEE Spectrum, 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference. Organize the data in a chart. Find the median, the first quartile, and the third quartile. Find the 65th percentile. Find the 10th percentile. Construct a box plot of the data. The middle 50% of the conferences last from _____ days to _____ days. Calculate the sample mean of days of engineering conferences. Calculate the sample standard deviation of days of engineering conferences. Find the mode. If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice. Give two reasons why you think that 3 - 5 days seem to be popular lengths of engineering conferences. Exercise 18 A survey of enrollment at 35 community colleges across the United States yielded the following figures (source: Microsoft Bookshelf): 6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622 Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency." Construct a histogram of the data. If you were to build a new community college, which piece of information would be more valuable: the mode or the average size? Calculate the sample average. Calculate the sample standard deviation. A school with an enrollment of 8000 would be how many standard deviations away from the mean? Exercise 19 The median age of the U.S. population in 1980 was 30.0 years. In 1991, the median age was 33.1 years. (Source: Bureau of the Census) What does it mean for the median age to rise? Give two reasons why the median age could rise. For the median age to rise, is the actual number of children less in 1991 than it was in 1980? Why or why not? Exercise 20 A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.  In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series. Which group is most likely to have an outlier? Explain how you determined that. Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other? Look at the BMW 5 series. Which quarter has the smallest spread of data? What is that spread? Look at the BMW 5 series. Which quarter has the largest spread of data? What is that spread? Look at the BMW 5 series. Find the Inter Quartile Range (IQR). Look at the BMW 5 series. Are there more data in the interval 31-38 or in the interval 45-55? How do you know this? Look at the BMW 5 series. Which interval has the fewest data in it? How do you know this? 31-35 38-41 41-64 Exercise 21 The following box plot shows the U.S. population for 1990, the latest available year. (Source: Bureau of the Census, 1990 Census)  Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)? How do you know? 12.6% are age 65 and over. Approximately what percent of the population are of working age adults (above age 17 to age 65)? Exercise 22 Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information:  EMBED Photoshop.Image.8 \s  How can you determine which survey was correct? Explain what the difference in the results of the surveys implies about the data. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?  If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilias sample? How do you know?  Exercise 23 Student grades on a chemistry exam were: { 77, 78, 76, 81, 86, 51, 79, 82, 84, 99} Construct a stem-and-leaf plot of the data. Are there any potential outliers? If so, which scores are they? Why do you consider them outliers? Try these multiple choice questions (Exercises 24 30). The next three questions refer to the following information. We are interested in the number of years students in a particular elementary statistics class have lived in California.  EMBED Photoshop.Image.8 \s  Exercise 24 What is the IQR? 8 11 15 35 Exercise 25 What is the mode? 19 19.5 14 and 20 22.65 Exercise 26 Is this a sample or the entire population? Sample Entire population Neither The next two questions refer to the following table. X = the number of days per week that 100 clients use a particular exercise facility.  EMBED Photoshop.Image.8 \s  Exercise 27 The 80th percentile is: 5 80 3 4 Exercise 28 The number that is 1.5 standard deviations BELOW the mean is approximately: 0.7 4.8 -2.8 Cannot be determined The next two questions refer to the following histogram. Suppose one hundred eleven people who shopped in a special T-shirt store were asked the number of T-shirts they own costing more than $19 each.  Exercise 29 The percent of people that own at most three (3) T-shirts costing more than $19 each is approximately: 21 59 41 Cannot be determined Exercise 30 If the data were collected by asking the first 111 people who entered the store, then the type of sampling is: Cluster Simple random Stratified Convenience Exercise 31 Below are the 2008 obesity rates by U.S. states and Washington, DC. (Source: http://www.cdc.gov/obesity/data/trends.html#State) State Percent State Percent Alabama 31.4Montana 23.9Alaska 26.1Nebraska 26.6Arizona 24.8Nevada 25Arkansas 28.7New Hampshire 24California 23.7New Jersey 22.9Colorado 18.5New Mexico 25.2Connecticut 21New York 24.4Delaware 27North Carolina 29Washington DC 21.8North Dakota 27.1Florida 24.4Ohio 28.7Georgia 27.3Oklahoma 30.3Hawaii 22.6Oregon 24.2Idaho 24.5Pennsylvania 27.7Illinois 26.4Rhode Island 21.5Indiana 26.3South Carolina 30.1Iowa 26South Dakota 27.5Kansas 27.4Tennessee 30.6Kentucky 29.8Texas 28.3Louisiana 28.3Utah 22.5Maine 25.2Vermont 22.7Maryland 26Virginia 25Massachusetts 20.9Washington 25.4Michigan 28.9West Virginia 31.2Minnesota 24.3Wisconsin 25.4Mississippi 32.8Wyoming 24.6Missouri 28.5 Construct a bar graph of obesity rates of your state and the four states closest to your state. Hint: The x-axis is labeled with the state names. Use a random number generator to randomly pick 8 states. 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rightOutsetlong8BIM( ?8BIM8BIM8BIM!SAdobe PhotoshopAdobe Photoshop CS8BIM".MM*bj(1r2iHHAdobe Photoshop CS Windows2008:08:21 07:41:41&(.HH (}tu{fiq@@ ),&'%&%%* ,*&*%&$)* *.**+*+/* .2-/..**/ 11+/*+).2 )(&&&&&&)  .~x~mw@@ $+%%%%%%, (*&)'&&** */+)*++/* )1+,--)). ,0*-+**.0 ('%%%%%%)  .ty`k@@ )+&&&'&&( **&'&'&** *.**(*+-* -1-...+++ /0+,+,+/. )'&&&&&&( ffffffffffffffffffffffffffffffffffffffffffffffffffffttftttfftttffttftttffHfHH HHHtHHHf tHHH tHHH HHHtH HHftHtHHHH tH tHHH tHHH HHHtH HHfff4HHHHHHHHttHftHHHtt HHHH4HHHHHHHHttHfHߜHHtt HHHHtHHHtt HHHHHHHHHHHHttHffHtf.HtHHtHtHߜft tttt Hߜt.HtHHtHtHߜfHHHtt Hߜtt tttt HߜtHtHHtHtHߜffftH HtHftttt߿tH HtHfHHtHttt߿tttt߿tH HtHffHHftHHt HtHf tHtHtt tHttHHt HtHftHHtHHtt tHt tHt Htt tHttHHt HtHffHtf0HHHtttHHHtftHtHHttH HHH0HHHtttHHHtfttHtttttH HHHtHtHHttH HHHHHHtttHHHtfffHHHH Hf tH HHtHHHHH HfHHtHHHtH tH HHtHHHHH 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FukkOle CompObjWObjInfoion Equation.2  xP LaserJet IIAll Adobe Photoshop ImageAdobe Photoshop Image9q Ole10Native$Ole10ItemName_1280809602_{?zCBũekkOle CompObjdObjInfoCONTENTS_1280808827!_{?zCBũekk8BPS8BIM%8BIM$ 4294967295 247 253 1 72/1 72/1 2 2008-08-21T07:40:35-06:00 2008-08-21T07:40:35-06:00 2008-08-21T07:40:35-06:00 Adobe Photoshop CS Windows adobe:docid:photoshop:3d546a5a-6f7e-11dd-93a7-e16d8c07c6eb application/vnd.adobe.photoshop 8BIMHH8BIM&?8BIM x8BIM8BIM 8BIM 8BIM' 8BIMH/fflff/ff2Z5-8BIMp8BIM@@8BIM8BIM5nullboundsObjcRct1Top longLeftlongBtomlongRghtlongslicesVlLsObjcslicesliceIDlonggroupIDlongoriginenum ESliceOrigin autoGeneratedTypeenum ESliceTypeImg boundsObjcRct1Top longLeftlongBtomlongRghtlongurlTEXTnullTEXTMsgeTEXTaltTagTEXTcellTextIsHTMLboolcellTextTEXT horzAlignenumESliceHorzAligndefault vertAlignenumESliceVertAligndefault bgColorTypeenumESliceBGColorTypeNone topOutsetlong leftOutsetlong bottomOutsetlong rightOutsetlong8BIM( ?8BIM8BIM8BIM!SAdobe PhotoshopAdobe Photoshop 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ttߢffttttttttttfttfffffHHffffffffffffffffffffffffffffffffffffffffffffffffffttttHttttftttHffHttt HtttttfttHHtffttttttttttttttttftttHffHttttttttttttttftttHߣfftHtHtHtH HttHtHtHtHftHttߣffttttttHtttttttttftttHffttttttHttttttttfttttfftHtttHtttttf ttߢffttttttttttftfffffHHfffffffffffffffffffffffffffffffffffffffffffffffHtttttttttftttff Httttt tttttftHHffttttttttt Htttttttttfttttfftttttttt tttttttttfttHtHߢff HttHtHtHtH ttHtHtHtHftH ttfftttttttttHHttttttttftttߣffHtttttttt tttttttttftttߣffHttttt"tttttf tHffttttttttttfttfffffHHffffffffffffffffffffffffffffffffffffffffffffffftttttttttftttff tttttttttfttHHff Htttttttttttttttttfttttff tttttttttttttttttfttttff ttHtHtHtHtHtHtHtHtHftHtHffHttttttttHttttttttfttttff tttttttttttttttttftttHߣff"ttttt%tHttttf ttHffttttttttttfttfffffHHfffffffffffffffffffffffffffffffffffffffffffffffttttHHtttfttHHffttttttttftttffttttttttttttttftttߢfftttttttttttttttfttttfftHtHtHtHtHtHtHtHtHftHtߡffttttttttHtttttttfttttffttttttttttttttftttߠff%tHttttttHtttf 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tttfftttttfttߢfffffHߺfffffffffffffffffffOle CompObj "dObjInfo#CONTENTSn Adobe Photoshop ImageAdobe Photoshop Image9q  Adobe Photoshop ImageAdobe Photoshop Image9q _08BPSu8BIM%8BIM$ 4294967295 415 117 1 72/1 72/1 2 2008-08-21T07:27:43-06:00 2008-08-21T07:27:43-06:00 2008-08-21T07:27:43-06:00 Adobe Photoshop CS Windows adobe:docid:photoshop:8a237013-6f7c-11dd-93a7-e16d8c07c6eb application/vnd.adobe.photoshop 8BIMHH8BIM&?8BIM x8BIM8BIM 8BIM 8BIM' 8BIMH/fflff/ff2Z5-8BIMp8BIM@@8BIM8BIM5uunullboundsObjcRct1Top longLeftlongBtomlonguRghtlongslicesVlLsObjcslicesliceIDlonggroupIDlongoriginenum ESliceOrigin autoGeneratedTypeenum ESliceTypeImg boundsObjcRct1Top longLeftlongBtomlonguRghtlongurlTEXTnullTEXTMsgeTEXTaltTagTEXTcellTextIsHTMLboolcellTextTEXT horzAlignenumESliceHorzAligndefault vertAlignenumESliceVertAligndefault bgColorTypeenumESliceBGColorTypeNone topOutsetlong leftOutsetlong bottomOutsetlong rightOutsetlong8BIM( ?8BIM8BIM8BIM!SAdobe PhotoshopAdobe Photoshop CS8BIM".MM*bj(1r2iHHAdobe 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HOMEWORKObjInfoA3CONTENTS_b1Table!SummaryInformation(D48BPSb8BIM%8BIM$ 4294967295 98 220 1 72/1 72/1 2 2008-08-21T08:34:15-06:00 2008-08-21T08:34:15-06:00 2008-08-21T08:34:15-06:00 Adobe Photoshop CS Windows adobe:docid:photoshop:d23fc692-6f85-11dd-93a7-e16d8c07c6eb application/vnd.adobe.photoshop 8BIMHH8BIM&?8BIM x8BIM8BIM 8BIM 8BIM' 8BIMH/fflff/ff2Z5-8BIMp8BIM@@8BIM8BIM5bbnullboundsObjcRct1Top longLeftlongBtomlongRghtlongbslicesVlLsObjcslicesliceIDlonggroupIDlongoriginenum ESliceOrigin autoGeneratedTypeenum ESliceTypeImg boundsObjcRct1Top longLeftlongBtomlongRghtlongburlTEXTnullTEXTMsgeTEXTaltTagTEXTcellTextIsHTMLboolcellTextTEXT horzAlignenumESliceHorzAligndefault vertAlignenumESliceVertAligndefault bgColorTypeenumESliceBGColorTypeNone topOutsetlong leftOutsetlong bottomOutsetlong rightOutsetlong8BIM( ?8BIM8BIM8BIM!SAdobe PhotoshopAdobe Photoshop CS8BIM".MM*bj(1r2iHHAdobe Photoshop CS Windows2008:08:21 08:34:15b&(.HH RVQOPVS  %$%' ##$' !!!%"" ! 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