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business statistics using excel

Introductory Statistics 7th Edition Prem S Mann - Solutions

3.80 Suppose the average credit card debt for households currently is $9500 with a standard deviation of $2600.a. Using Chebyshev’s theorem, find at least what percentage of current credit card debts for all households are between i. $4300 and $14,700 ii. $3000 and $16,000*b. Using Chebyshev’s
3.79 The 2009 gross sales of all companies in a large city have a mean of $2.3 million and a standard deviation of $.6 million. Using Chebyshev’s theorem, find at least what percentage of companies in this city had 2009 gross sales ofa. $1.1 to $3.5 millionb. $.8 to $3.8 millionc. $.5 to $4.1
3.78 The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation of 20 minutes. Using Chebyshev’s theorem, find the percentage of runners who ran this road race ina. 180 to 260 minutesb. 160 to 280 minutesc. 170 to 270 minutes
3.77 A sample of 3000 observations has a mean of 82 and a standard deviation of 16. Using the empirical rule, find what percentage of the observations fall in the intervals , and
3.76 A large population has a mean of 310 and a standard deviation of 37. Using the empirical rule, find what percentage of the observations fall in the intervals and
3.75 A large population has a mean of 230 and a standard deviation of 41. Using Chebyshev’s theorem, find at least what percentage of the observations fall in the intervals and
3.74 A sample of 2000 observations has a mean of 74 and a standard deviation of 12. Using Chebyshev’s theorem, find at least what percentage of the observations fall in the intervals and. Note that here represents the interval to and so on.
3.73 Briefly explain the empirical rule. To what kind of distribution is it applied?
3.72 Briefly explain Chebyshev’s theorem and its applications.
*3.60 Consider the following two data sets.Data Set I: 4 8 15 9 11 Data Set II: 8 16 30 18 22 Note that each value of the second data set is obtained by multiplying the corresponding value of the first data set by 2. Calculate the standard deviation for each of these two data sets using the formula
*3.59 Consider the following two data sets.Data Set I: 12 25 37 8 41 Data Set II: 19 32 44 15 48 Note that each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. Calculate the standard deviation for each of these two data sets using the formula
*3.58 The SAT scores of 100 students have a mean of 975 and a standard deviation of 105. The GPAs of the same 100 students have a mean of 3.16 and a standard deviation of .22. Is the relative variation in SAT scores larger or smaller than that in GPAs?
*3.57 One disadvantage of the standard deviation as a measure of dispersion is that it is a measure of absolute variability and not of relative variability. Sometimes we may need to compare the variability of two different data sets that have different units of measurement. The coefficient of
3.56 The following data are the ages (in years) of six students.19 19 19 19 19 19 Calculate the standard deviation. Is its value zero? If yes, why?
3.55 The following data give the hourly wage rates of eight employees of a company.$22 22 22 22 22 22 22 22 Calculate the standard deviation. Is its value zero? If yes, why?
3.54 The following data represent the 2006 guaranteed annual salaries (in thousands of dollars) of the head coaches of the final eight teams in the 2006 NCAA Men’s Basketball Championship. The data are given in the following order: Connecticut, Florida, George Mason, LSU, Memphis, Texas, UCLA,
3.53 The following data represent the total points scored in each of the NFL championship games played from 2000 through 2009 in that order.39 41 37 69 61 45 31 46 31 50 Compute the variance, standard deviation, and range for these data.
3.52 The following data give the numbers of hours spent partying by 10 randomly selected college students during the past week.7 1 45 0 9 7 1 04 0 8 Compute the range, variance, and standard deviation.
3.51 Following are the temperatures (in degrees Fahrenheit) observed during eight wintry days in a midwestern city:23 14 6 7 2 11 16 19 Compute the range, variance, and standard deviation.
3.50 The following data give the number of hot dogs consumed by 10 participants in a hot-dog-eating contest.21 17 32 8 20 15 17 23 9 18 Calculate the range, variance, and standard deviation for these data.
3.49 Attacks by stinging insects, such as bees or wasps, may become medical emergencies if either the victim is allergic to venom or multiple stings are involved. The following data give the number of patients treated each week for such stings in a large regional hospital during 13 weeks last
3.48 The following data give the number of highway collisions with large wild animals, such as deer or moose, in one of the northeastern states during each week of a 9-week period.7 1 03 8 2 5 7 4 9 Find the range, variance, and standard deviation.
3.47 The following data give the numbers of pieces of junk mail received by 10 families during the past month.41 33 28 21 29 19 14 31 39 36 Find the range, variance, and standard deviation.
3.45 The following data give the numbers of car thefts that occurred in a city in the past 12 days.6 3 7 1 14 3 8 7 2 6 9 1 5 Calculate the range, variance, and standard deviation.3.46 Refer to the data in Exercise 3.23, which contained the numbers of tornadoes that touched down in 12 states that
3.44 The following data give the prices of seven textbooks randomly selected from a university bookstore.$89 $170 $104 $113 $56 $161 $147a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero?b. Calculate the range, variance,
3.43 The following data give the number of shoplifters apprehended during each of the past 8 weeks at a large department store.7 1 08 3 1 51 26 1 1a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero?b. Calculate the range,
3.42 The following data set belongs to a sample:14 18 1 08 8 16 Calculate the range, variance, and standard deviation.
3.41 The following data set belongs to a population:5 7 2 0 9 1 61 07 Calculate the range, variance, and standard deviation.
3.40 Briefly explain the difference between a population parameter and a sample statistic. Give one example of each.
3.39 When is the value of the standard deviation for a data set zero? Give one example. Calculate the standard deviation for the example and show that its value is zero.
3.38 Can the standard deviation have a negative value? Explain.
3.37 The range, as a measure of spread, has the disadvantage of being influenced by outliers. Illustrate this with an example.
*3.36 When studying phenomena such as inflation or population changes that involve periodic increases or decreases, the geometric mean is used to find the average change over the entire period under study.To calculate the geometric mean of a sequence of n values x1, x2,..., xn, we multiply them
*3.35 In some applications, certain values in a data set may be considered more important than others.For example, to determine students’ grades in a course, an instructor may assign a weight to the final exam that is twice as much as that to each of the other exams. In such cases, it is more
*3.34 The following data give the prices (in thousands of dollars) of 20 houses sold recently in a city.184 297 365 309 245 387 369 438 195 390 323 578 410 679 307 271 457 795 259 590 Find the 20% trimmed mean for this data set.
*3.33 The trimmed mean is calculated by dropping a certain percentage of values from each end of a ranked data set. The trimmed mean is especially useful as a measure of central tendency when a data set contains a few outliers at each end. Suppose the following data give the ages (in years) of 10
*3.32 Consider the following two data sets.Data Set I: 4 8 15 9 11 Data Set II: 8 16 30 18 22 Notice that each value of the second data set is obtained by multiplying the corresponding value of the first data set by 2. Calculate the mean for each of these two data sets. Comment on the relationship
*3.31 Consider the following two data sets.Data Set I: 12 25 37 8 41 Data Set II: 19 32 44 15 48 Notice that each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. Calculate the mean for each of these two data sets. Comment on the relationship
*3.30 Seven airline passengers in economy class on the same flight paid an average of $361 per ticket.Because the tickets were purchased at different times and from different sources, the prices varied. The first five passengers paid $420, $210, $333, $695, and $485. The sixth and seventh tickets
*3.29 The mean age of six persons is 46 years. The ages of five of these six persons are 57, 39, 44, 51, and 37 years, respectively. Find the age of the sixth person.
*3.28 The mean 2009 income for five families was $99,520. What was the total 2009 income of these five families?
*3.27 For any data, the sum of all values is equal to the product of the sample size and mean; that is,. Suppose the average amount of money spent on shopping by 10 persons during a given week is $105.50. Find the total amount of money spent on shopping by these 10 persons.
*3.26 Twenty business majors and 18 economics majors go bowling. Each student bowls one game. The scorekeeper announces that the mean score for the 18 economics majors is 144 and the mean score for the entire group of 38 students is 150. Find the mean score for the 20 business majors.
*3.25 One property of the mean is that if we know the means and sample sizes of two (or more) data sets, we can calculate the combined mean of both (or all) data sets. The combined mean for two data sets is calculated by using the formula where n1 and n2 are the sample sizes of the two data sets
3.24 The following data set lists the number of women from each of 10 different countries who were on the Rolex Women’s World Golf Rankings Top 25 list as of March 31, 2009. The data, entered in that order, are for the following countries: Australia, Brazil, England, Japan, Korea, Mexico, Norway,
3.23 The following data represent the numbers of tornadoes that touched down during 1950 to 1994 in the 12 states that had the most tornadoes during this period (Storm Prediction Center, 2009). The data for these states are given in the following order: CO, FL, IA, IL, KS, LA, MO, MS, NE, OK, SD,
3.22 The Tri-City School District has instituted a zero-tolerance policy for students carrying any objects that could be used as weapons. The following data give the number of students suspended during each of the past 12 weeks for violating this school policy.1 59 1 21 17 6 9 1 01 43 6 5 Calculate
3.21 Nixon Corporation manufactures computer monitors. The following data are the numbers of computer monitors produced at the company for a sample of 10 days.24 32 27 23 35 33 29 40 23 28 Calculate the mean, median, and mode for these data.
3.20 A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights, blankets, and so forth) in their vehicles for emergency use while driving in winter. The following data give the number of items out of these 12 that were carried
3.19 Due to antiquated equipment and frequent windstorms, the town of Oak City often suffers power outages. The following data give the numbers of power outages for each of the past 12 months.4 5 7 3 2 0 2 3 2 1 2 4 Compute the mean, median, and mode for these data.
3.18 The following table gives the number of major penalties for each of the 15 teams in the Eastern Conference of the National Hockey League during the 2008–09 season (NHL, 2009). A major penalty is subject to 5 minutes in the penalty box for a player.Number of Team Major Penalties Philadelphia
3.17 The following data give the revenues (in millions of dollars) for the last available fiscal year for a sample of six charitable organizations for serious diseases (Charity Navigator, 2009). The values are, listed in order, for the Alzheimer’s Association, the American Cancer Society, the
3.16 The following data give the numbers of car thefts that occurred in a city during the past 12 days.6 3 7 11 4 3 8 7 2 6 9 15 Find the mean, median, and mode.
3.15 The following data give the 2006–07 team salaries for 20 teams of the English Premier League, arguably the best-known soccer league in the world. The salaries are given in the order in which the teams finished during the 2006–07 season. The salaries are in millions of British pounds (note
3.14 The following data give the 2008 profits (in millions of dollars) of the six Arizona-based companies for the year 2008 (Fortune, May 5, 2008). The data represent the following companies, respectively:Freeport-McMoRan Copper & Gold, Avnet, US Airways Group, Allied Waste Industries, Insight
3.13 The following data give the 2007 gross domestic product (GDP) in billions of dollars for all 50 states.The data are entered in alphabetic order by state (Bureau of Economic Analysis, June 2005).166 45 247 95 1813 236 216 60 735 397 62 51 610 246 129 117 154 216 48 269 352 382 255 89 229 34 80
3.12 Refer to the data table in Exercise 3.11. Calculate the mean and median for the data on personal exemptions for these states.
3.11 The following table gives the standard deductions and personal exemptions for persons filing with“single” status on their 2009 state income taxes in a random sample of 10 states. Calculate the mean and median for the data on standard deductions for these states.Standard Deduction Personal
3.10 The following data set belongs to a sample:14 18 1 08 8 16 Calculate the mean, median, and mode.
3.9 The following data set belongs to a population:5 7 2 0 9 16 10 7 Calculate the mean, median, and mode.
3.8 Prices of cars have a distribution that is skewed to the right with outliers in the right tail. Which of the measures of central tendency is the best to summarize this data set? Explain.
3.7 Explain the relationships among the mean, median, and mode for symmetric and skewed histograms.Illustrate these relationships with graphs.
3.6 Is it possible for a (quantitative) data set to have no mean, no median, or no mode? Give an example of a data set for which this summary measure does not exist.
3.5 Which of the three measures of central tendency (the mean, the median, and the mode) can assume more than one value for a data set? Give an example of a data set for which this summary measure assumes more than one value.
3.4 Which of the three measures of central tendency (the mean, the median, and the mode) can be calculated for quantitative data only, and which can be calculated for both quantitative and qualitative data?Illustrate with examples.
3.3 Using an example, show how outliers can affect the value of the mean.
3.2 Briefly explain the meaning of an outlier. Is the mean or the median a better measure of central tendency for a data set that contains outliers? Illustrate with the help of an example.
3.1 Explain how the value of the median is determined for a data set that contains an odd number of observations and for a data set that contains an even number of observations.
TA2.13 Make a dotplot for the data of Exercise 2.65.
TA2.12 Make a dotplot for the data of Exercise 2.64.
TA2.11 Make a pie chart for the frequency distribution obtained in Exercise 2.29.
TA2.10 Make a pie chart for the frequency distribution obtained in Exercise 2.19.
TA2.9 Prepare a bar graph for the frequency distribution obtained in Exercise 2.29.
TA2.8 Prepare a bar graph for the frequency distribution obtained in Exercise 2.28.
TA2.7 Prepare a stem-and-leaf display for the data of Exercise 2.53.
TA2.6 Prepare a stem-and-leaf display for the data given in Exercise 2.48.
TA2.5 Construct a histogram for the data from Exercise 2.20 on the numbers of computer keyboards assembled. Use the classes given in that exercise. Use the midpoints to mark the horizontal axis in the histogram.
TA2.4 Refer to Data Set I that accompanies this text on the prices of various products in different cities across the country. Select a subsample of 60 from the column that contains information on pizza prices and then construct a histogram for these data.
TA2.3 Refer to Data Set V that accompanies this text (see Preface and Appendix B) on the times taken to run the Manchester Road Race for a sample of 500 participants. From that data set, select the 6th value, and then select every 10th value after that (i.e., select the 6th, 16th, 26th, 36th, . . .
TA2.2 Construct a bar graph and a pie chart for the frequency distribution prepared in Exercise 2.6.
TA2.1 Construct a bar graph and a pie chart for the frequency distribution prepared in Exercise 2.5.
11. Choose 15 of each of two types of magazines (news, sports, fitness, entertainment, and so on) and record the percentage of pages that contain at least one advertisement. Using these percentages and the types of magazines, write a brief report that covers the following:a. Prepare an appropriate
10. Using the data you gathered for the mini-project in Chapter 1, prepare a summary of that data set that includes the following.a. Prepare an appropriate type of frequency distribution table for one of the quantitative variables and then compute relative frequencies and cumulative relative
9. Make a dotplot for the data given in Problem 5.
8. Consider this stem-and-leaf display:3 0 3 7 4 2 4 6 7 9 5 1 3 3 6 6 0 7 7 7 1 9 Write the data set that was used to construct this display.
7. Construct a stem-and-leaf display for the following data, which give the times (in minutes) 24 customers spent waiting to speak to a customer service representative when they called about problems with their Internet service provider.12 15 7 29 32 16 10 14 17 8 19 21 4 14 22 25 18 6 22 16 13 16
6. Refer to the frequency distribution prepared in Problem 5. Prepare the cumulative percentage distribution using that table. Draw an ogive for the cumulative percentage distribution.
5. A large Midwestern city has been chronically plagued by false fire alarms. The following data set gives the number of false alarms set off each week for a 24-week period in this city.10 4 8 7 3 7 10 2 6 12 11 8 1 6 5 13 9 7 5 1 14 5 15 3a. Construct a frequency distribution table. Take 1 as the
4. Twenty elementary school children were asked if they live with both parents (B), father only (F), mother only (M), or someone else (S). The responses of the children follow.M B B M F S B M F M B F B M M B B F B Ma. Construct a frequency distribution table.b. Write the relative frequencies and
3. Briefly explain and illustrate with the help of graphs a symmetric histogram, a histogram skewed to the right, and a histogram skewed to the left.
2. The following table gives the frequency distribution of times (to the nearest hour) that 90 fans spent waiting in line to buy tickets to a rock concert.Waiting Time(hours) Frequency 0 to 6 5 7 to 13 27 14 to 20 30 21 to 27 20 28 to 34 8 Circle the correct answer in each of the following
1. Briefly explain the difference between ungrouped and grouped data and give one example of each type.
2.97 CBS Sports had a Facebook page for the 2009 NCAA Men’s Basketball Tournament including bracket contests, discussion sites, and a variety of polls. One of the polls asked users to identify their most despised teams. The following pie chart (Figure 2.28) gives a breakdown of the votes by the
2.96 Figure 2.27 contains stacked dotplots of 2007 state obesity rates by different geographic regions—Midwest, Northeast, South, and West.a. Which region has the least variability (greatest consistency) of obesity rates? Which region has the most variability (least consistency) of obesity rates?
2.95 Table 2.18 contains the differences in the obesity rates (called rate change in the table) for the years between 2007 and 1997 for each of the 50 states and the District of Columbia. The obesity rate is the percentage of people having a body mass index (BMI) of 30 or higher. Figure 2.26
2.94 The following table lists the earnings per event that were referred to in Exercise 2.93. Although the table lists earnings per event, players are listed in order of their total earnings, not their earnings per event.Note that men and women are ranked together in the table.Earnings per Event
2.93 Stem-and-leaf displays can be used to compare distributions for two groups using a back-to-back stem-and-leaf display. In such a display, one group is shown on the left side of the stems, and the other group is shown on the right side. When the leaves are ordered, the leaves increase as one
2.92 The pie chart in Figure 2.24 shows the percentage distribution of ages (i.e., the percentages of all prostate cancer patients falling in various age groups) for men who were recently diagnosed with prostate cancer.a. Are more or fewer than 50% of these patients in their 50s? How can you
2.91 Refer to the data on weights of 44 college students given in Exercise 2.89. Create a dotplot of all 44 weights. Then create stacked dotplots for the weights of male and female students. Describe the similarities and differences in the distributions of weights of male and female students. Using
2.90 Consider the two histograms given in Figure 2.23, which are drawn for the same data set. In this data set, none of the values are integers.Supplementary Exercises 67 Figure 2.23 Two histograms for the same data.a. What are the endpoints and widths of classes in each of the two histograms?b. In

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