21 Collect the closing price of two stocks over a period of 10 sessions. Calculate the coefficients of variation for the two data sets and then check which stock is more risky.
22 The following data give the number of physicians who work in a hospital and are classified according to their age:Age[35–40)[40–45)[45–50)[50–55)[55–60)[60–65]Frequency607568729055Find the mean and the standard deviation for this set of grouped data.
23 Prepare a frequency table for the data in Problem 9 of Section 2.4. Find the mean and the variance for the grouped and the ungrouped data. Then compare the values of the mean and variance of the grouped and the ungrouped data.
24 The following data give lengths (in mm) of a type of rods used in car engines.128118120124135130128116122120118125127123126124120132131119117124129131133115121122127127134128132135125120121126124123Determine the quartiles () for this data.Find the IQR for these data.Determine the value of the 70th percentile for these data.What percentage of the data falls between and ?
25 Compute , , and for the data in Problem 24. Then,Find the number of data points that fall in the intervals , , and Verify whether the empirical rule holds for these data.
26 A car manufacturer wants to achieve 35 miles/gal on a particular model. The following data give the gas mileage (rounded to the nearest mile) on 40 randomly selected brand‐new cars of that model. Each car uses regular unleaded gasoline:34333632333435373233323134373233333634 3135363533323234353430343735323134323332 33Find the mean and the standard deviation for these data.Check whether the empirical rule holds for these data.
27 Refer to the data in Problem 26. Determine the following:The values of the three quartiles , and .The IQR for these data.Construct a box‐plot for these data and verify if the data contains any outliers.
28 The following data give the test scores of 57 students in an introductory statistics class:687892808779748586889197717281866040767720998079898787808395929887869596757679808581777684828356686991886975745961Find the values of three quartiles , and .Find the IQR for these data.Construct the box plot for these data and check whether the data is skewed.Do these data contain any outliers?
29 The following data give the overtime wages (in dollars) earned on a particular day by a group of 40 randomly selected employees of a large manufacturing company:30354550253036384240463630352446425040403534343028323026283640424038383645403642Find the IQR for these data.Count what percentage of the data falling between the first and the third quartiles.Do you think the result in part (b) agrees with your expectations?
30 The following data give the time (in minutes) taken by 20 students to complete a class test:5563705862715070606559626671587075706568Find the mean, median, and mode for these data.Use values of the mean, median, and mode to comment on the shape of the frequency distribution of these data.
31 The following data give the yearly suggested budget (in dollars) for undergraduate books by 20 randomly selected schools from the whole United States:690650800750675725700690650900850825910780860780850870750875Find the mean and the standard deviation for these data.What percentage of schools has their budget between and ?
32 A data set has a mean of 120 and a standard deviation of 10. Using the empirical rule, find what percentage of data values fall:Between 110 and 130.Between 100 and 140.Between 90 and 150.
33 Suppose that the manager of a pulp and paper company is interested in investigating how many trees are cut daily by one of its contractors. After some investigation, the manager finds that the number of trees cut daily by that contractor forms a bell shaped distribution with mean 90 and standard deviation 8. Using the empirical rule, determine the percentage of the days he cutsBetween 82 and 98 trees.Between 66 and 114 trees.More than 106 trees.Less than 74 trees.
34 The following sample data give the number of pizzas sold by a Pizza Hut over a period of 15 days:754580908590928695959086949978Prepare a box plot for these data and comment on the shape of this data set.Find the mean, median, and standard deviation of these data.
35 The following sample data give the GRE scores (actual score—2000) of 20 students who have recently applied for admission to the graduate program in an engineering school of a top‐rated US university:268320290310300270250268330290240269295325316320299286269250Find the sample mean and the sample standard deviation .Determine the percentage of the data that falls in the interval .Determine the range of the middle 50% of the observations.
36 Assume that the data in Problem 35 come from a population having a bell‐shaped probability distribution. Then, using the empirical rule, determine how many data values one would expect to fall within the intervals and . Compare your results with the actual number of data values that fall in these intervals. Also, using technology, verify the assumption that the observations come from a population having a bell shaped probability distribution.
37 The following data give the number of defective parts received in the last 15 shipments at a manufacturing plant:8101211139151410161812141613Find the mean of these data.Find the standard deviation of these data.Find the coefficient of variation for these data.
38 The owner of the facility in Problem 37 has another plant where the shipments received are much larger than at the first plant. The quality engineer at this facility also decides to collect the data on defectives received in each shipment. The last 15 shipments provided the following data:213038475839351559604347393041Find the mean and the standard deviation of these data.Find the coefficient of variation of these data, compare it with the one obtained in Problem 37, and comment on which facility receives more stable shipments.
39 Prepare box plots for the data in Problems 37 and 38. Comment on the shape of the distribution of these two data sets.
40 The following data give the test scores of 40 students in a statistics class:68789280877974858688919771728186604076772099807989878780839592988786959676757980Find the sample mean and the sample standard deviation S for these data.Prepare a frequency distribution table for these data.Use the grouped data in part (b) to determine the grouped mean and the grouped standard deviation .Compare the values of and with the values of and the standard deviation . Notice that the grouped mean and grouped standard deviations are only the approximate values of the actual mean and standard deviations of the original (i.e., ungrouped) sample.
41 The following two data sets give the number of defective ball bearings found in 20 boxes randomly selected from two shipments:Shipment I6065797167687356596366597277796971706055Shipment II4555565059604838424137575549433945515355Find the quartiles for each of these two sets.Prepare the box plots for each of the two data sets and display them side by side on one sheet of graph paper.Use part (b) to compare the two shipments. Which shipment in your opinion is of better quality?
42 The following data give the number of flights that left late at a large airport over the past 30 days:5059633012055494743514751576258503953504543465259483651334232Prepare a complete frequency distribution table for these data.Prepare a box plot for these data to comment on the shape of the distribution of these data. Does the set contain any outliers?Find the mean and the standard deviation for these data.
43 The following data gives the inflation rate and interest rates in the United States over 10 consecutive periods. Determine the correlation coefficient between the inflation rate and the interest rates in the United States. Interpret the value of the correlation coefficient you determined.Period12345678910Inflation rate2.342.542.222.671.983.222.512.572.752.67Interest rate4.554.654.754.824.464.854.354.254.554.35
44 The following data gives the heights (in.) and weights (lb) of eight individuals. Determine the correlation coefficient between the heights and weights. Interpret the value of the correlation coefficient you have determined.Individuals12345678Heights 77 72 73 76 72 73 77 72Weights156172195181158164164191
45 It is generally believed that students' performance on a test is related to