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 are large, all one has to do is to subtract a constant from each of the data points and then find the standard deviation for the new data. The standard deviation of the new data, usually called the coded data, is exactly the same as that of the original data. Thus, for example, in Problem 20, one can subtract 567 (the smallest data point) from each data point and then find the standard deviation of the set of the coded data. Try it.
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,
