Do the followings:
1 Construct box plots for the three sets of data, that is, from machine‐1, machine‐2, and machine‐3, and compare average values of the diameter of the parts produced by the three machines.
2 Determine the variances for the three sets of data, compare them, and write your conclusions.
3 Determine the coefficient of variation for the three sets of data, compare them, and write your conclusions.
4 Compare your conclusions in Parts 2 and 3 above, and comment.
2.11 Using JMP
This section is available for download from the book website: www.wiley.com/college/gupta/statistics2e.
Review Practice Problems
1 During a flu season, it is common that many workers cannot come to work because either they themselves are sick or they have to take care of their sick children. The following data give the number of employees of a company who did not come to work on 18 days during a flu season:7, 5, 10, 12, 6, 7, 8 10, 3, 16, 10, 9, 8, 10, 9, 8, 7, 6Construct a dot plot for these data. Comment on what you learn from the dot plot.
2 A saving and loan institution wants to find how many of their customers default their loan payments. The following data give the number of customers who did not make their payment on time at least once over the past 12 months:15, 20, 18, 16, 3, 19, 14, 17, 17, 16, 30, 15Construct a dot plot for these data. Comment on any patterns you observe in these data.
3 The following data give the number of machines in a shoe factory that had breakdowns during the past 21 shifts:3, 2, 1, 0, 2, 1, 4, 2, 0, 1, 2, 3, 1, 0, 4, 2, 1, 10, 2, 1, 2Construct a dot plot for these data. If you were the maintenance engineer, what would you learn from these data?
4 The following data classify a group of students who are attending a seminar on environmental issues by their class standing:Class standingFrequencyFreshmen16Sophomore18Junior20Senior15Graduate30Construct a bar chart for these data.Construct a pie chart for these data.
5 Suppose there are two fund‐raising concerts at a university. The following data give the number of students by their class standing who attended one or the other of the concerts:Class standingFrequency‐1Frequency‐1Freshmen1640Sophomore1830Junior2021Senior1520Graduate3015Construct a side‐by‐side bar chart for each of the concert and compare the two sets of data.Construct pie charts for each of the concerts. Do you think you can get the same information by using the two pie charts, as by using the side‐by‐side bar charts?
6 Refer to the data in Problem 15 of Section 2.4.Construct a frequency histogram for these data.Construct a relative‐frequency histogram for these data.
7 Suppose that in a midwestern state, a legislator running for governor proposes the following state budget (in millions of dollars) for the following year:Education900Medicaid400Other social programs500Road and bridges350Agriculture400Others250Use JMP, MINITAB, or R to do the following:Construct a bar chart for these data.Construct a pie chart for these data.Determine what percentage of the budget is used for all social programs.
8 The following data give the number of defective parts produced in 21 consecutive shifts of 1 wk15141816171327141510301481415171513141620Prepare a line graph of these data.Check if any peaks or dips appear in the line graph.As a quality manager of the company, what would you conclude from this line graph, and what will be your line of action to reduce the number of defective parts produced?
9 Consider the following stem‐and‐leaf diagram:StemLeaf32 5 740 3 6 8 951 2 2 7 863 5 6 6 9 971 5 5 7 8Reproduce the data set represented by the diagram.
10 The following data give the number of employees from 19 different sectors of a large company who were absent for at least two days from a certain training program:75101267810316109810769112Construct a dot plot for these data and comment on what you observe in these data.
11 To improve the quality of a crucial part used in fighter jets, a quality control engineer is interested in finding the type of defects usually found in that part. He labels these defects as A, B, C, D, and E based on severity of the defect. The following data show the type of defects found in the defective parts:BDABCDBEBEDBCBECDBEDBCBDBCDBABCBDEBEBECBDEBCEBEBCBDBPrepare a bar chart for these data, and comment on the types of defects encountered in the parts under study.
12 The following data give the salaries (in thousands of dollars) of 62 randomly selected engineers from different manufacturing companies located in different regions of the United States:654585689895586264545758851204556150140123655566768845506066554648985666185565577596714516667586869878992858877697686815414515419020585Prepare a box whisker plot for these data.Do these data contain any mild or extreme outliers?
13 The following data give the number of cars owned by 50 randomly selected families in a metropolitan area:35212431234232531243212145123234231232423213124232Construct a single‐valued frequency distribution table for these data.Compute the columns of relative frequencies and percentages.Construct a bar chart for these data.What percentage of the families own at least 3 cars?What percentage of the families own at most 2 cars?
14 The following data give the total cholesterol levels (mg/100 mL) of 100 US males between 35 to 65 years of age:177196150167175162195200167170179172176179177153177189185167151177191177175151173199167197188163174151183174177200182195160151177154150180170172153152194197192155174159193182175169180200194182188152196198171176200180161182188168165168160175193159183166198184172180195199156158152174151173166183194156Construct a frequency distribution table with classes [150, 160), [160, 170), What percentage of US males between 35 to 65 years of age do you estimate have cholesterol levels higher than 200 mg/100 mL?What percentage of US males between 35 to 65 years of age do you estimate have cholesterol levels less than 180 mg/100 mL?
15 We know that from a grouped data set we cannot retrieve the original data. Generate a new (hypothetical) data set from the frequency distribution table that you prepared in Problem 14. Reconstruct a frequency distribution table for the new set and comment on whether the two frequency tables should be different or not.
16 A group of dental professionals collected some data on dental health and concluded that 10% of the Americans have zero or one cavity, 50% have two or three cavities, 30% have four cavities, and rest of the 10% have five or more cavities. Construct a pie chart that describes the dental health of the American population.
17 Find the mean, median, and mode for the following sample data on credit hours for which students are registered in a given semester:7118127614171513
18 The following data give hourly wages of 20 workers randomly selected from a chipmaker company:1612181523292120212518272125221624262126Determine the mean, median, and mode for these data. Comment on whether these data are symmetric or skewed.
19 The following data give daily sales (in gallons) of gasoline at a gas station during April:414450380360470400411465390384398412416454459395430439449453464450380398410399416426430425Find the mean, median, and mode for these data. Comment on whether these data are symmetric, left skewed, or right skewed.Find the range, variance, standard deviation, and the coefficient of variation for these data.
20 The owner of the gas station of Problem 19 also owns another gas station. He decided to collect similar data for the second gas station during the same period. These data are given below.570590600585567570575580577583589585595570574576581583595591585583580597599600577573574579Find the range, variance, standard deviation, and coefficient of variation for these data.Compare the standard deviations for the two data sets.Do you think it will be more prudent to compare the coefficients of variation rather than the two standard deviations? Why or why not?Sometimes the observations in a given data set are too large numerically to compute the standard deviation easily. However, if these observations are small, particularly when we are using paper, pen, and a small calculator, then there is little problem in computing the standard deviation. If observations