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intro stats
Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions
Placement exams An incoming freshman took her college’s placement exams in French and mathematics.In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12. On
Temperatures A town’s January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°? Explain.
Mensa People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be considered a genius?
Stats test The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor’s z-score was -2. How many points did he score?
In the 2010 Winter Olympics men’s slalom, Li Lei of China skied in a total time of 120.86 sec for two runs—about 1 standard deviation slower than the mean.If a Normal model is useful in describing slalom times, about how many of the 48 skiers finishing the event would you expect skied the
Many colleges and universities require applicants to submit scores on standardized tests such as the SAT Writing, Math, and Critical Reading (Verbal)tests. The college your little sister wants to apply to says that while there is no minimum score required, the middle 50% of their students have
The times in the men’s combined event at the winter Olympics are reported in minutes and seconds. The mean and standard deviation of the 34 final super combined times at the 2010 Olympics were 168.93 seconds and 2.90 seconds, respectively.Question: Suppose instead that we had reported the times
At the 2010 Vancouver Winter Olympics, Bode Miller had earlier earned a bronze medal in the downhill and a silver medal in the super-G slalom before winning the gold in the men’s super combined. Ted Ligety, the winner of the gold medal at the 2006 games, had super combined times in 2010 of 50.76
The men’s super combined skiing event debuted in the 2010 Winter Olympics in Vancouver. It consists of two races: a downhill and a slalom. Times for the two events are added together, and the skier with the lowest total time wins. At Vancouver, the mean slalom time was 52.67 seconds with a
Stereograms, revisited Because of the skewness of the distributions of fusion times described in Exercise 51, we might consider a re-expression. Here are the boxplots of the log of fusion times. Is it better to analyze the original fusion times or the log fusion times? Explain. 1.6 1.2 0.8 0.4 Log
Stereograms Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An experiment was performed to determine whether knowledge of the embedded
Rainmakers The table lists the amount of rainfall (in acre-feet) from the 26 clouds seeded with silver iodide discussed in Exercise 40:a) Why is acre-feet a good way to measure the amount of precipitation produced by cloud seeding?b) Plot these data, and describe the distribution.c) Create a
Assets again Here are the same data you saw in Exercise 47 after re-expressions as the square root of assets(in $M) and the logarithm of assets (in $M):a) Which re-expression do you prefer? Why?b) In the square root re-expression, what does the value 50 actually indicate about the company’s
Music library Students were asked how many songs they had in their digital music libraries. Here’s a display of the responses:a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread?b) What would you suggest doing with these data if we want to
Assets Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list of the nation’s top corporations:a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread?b) What would you suggest doing with these data if
Drunk driving Accidents involving drunk drivers account for a large portion of all deaths on the nation’s highways.The table in the next column tracks the number of alcohol-related fatalities for 31 years.a) Create a stem-and-leaf display or a histogram of these data.b) Create a timeplot.c) Using
Fruit flies Researchers tracked a population of 1,203,646 fruit flies, counting how many died each day for 171 days.Here are three timeplots offering different views of these data. One shows the number of flies alive on each day, one the number who died that day, and the third the mortality
Baseball 2013 American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The League believes that replacing the pitcher, typically a weak hitter, with another player in the batting order produces more runs and generates more interest among
MPG A consumer organization wants to compare gas mileage figures for several models of cars made in the United States with autos manufactured in other countries.The data for a random sample of cars classified as “midsize”are shown in the table.a) Create graphical displays for these two
Cholesterol and Smoking A study examining the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no more than 5 years and then stopped. Create appropriate graphical displays for both groups, and write
Industrial experiment Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running 10 boards at each of two different speeds. To assess the results, they measured the distance (in
Cloud seeding In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 58 clouds were randomly assigned to be seeded or not.The amount of rain they generated was then measured(in acre-feet). Here are the summary statistics:a) Which of the summary statistics are
Reading scores A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for the 14 boys and 11 girls are shown:a) Which group had the highest score?b) Which group had the greater range?c) Which group had the greater
Cholesterol The Framingham Heart Study recorded the cholesterol levels of more than 1400 men. Here is an ogive of the distribution of these cholesterol measures.(An ogive shows the percentage of cases at or below a certain value.) Construct a boxplot for these data, and write a few sentences
Derby speeds 2014 (Data in Kentucky Derby 2014)How fast do horses run? Kentucky Derby winners top 30 miles per hour, as shown in this graph. The graph shows the percentage of Derby winners that have run slower than each given speed. Note that few have won running less than 33 miles per hour, but
SAT scores Here are the summary statistics for Verbal SAT scores for a high school graduating class:a) Create side-by-side boxplots comparing the scores of boys and girls as best you can from the information given.b) Write a brief report on these results. Be sure to discuss the shape, center, and
Caffeine A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixture of the two (getting a half-dose of caffeine). Here are the 5-number summaries
Vineyards revisted Here are summary statistics for the sizes (in acres) of the Finger Lakes vineyards (of Exercise 3.17):Suppose you didn’t have access to the data. answer the following questions from the summary statistics alone:a) Would you describe this distribution as symmetric or skewed?
Graduation? A survey of major universities asked what percentage of incoming freshmen usually graduate “on time” in 4 years. Use the summary statistics given to answer the questions that follow.a) Would you describe this distribution as symmetric or skewed? Explain.b) Are there any outliers?
Eye and hair color A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:The Statistics students analyzing the data were asked to
Test scores Three Statistics classes all took the same test.Histograms and boxplots of the scores for each class are shown below. Match each class with the corresponding boxplot. # of Students 2 4 30 60 Class 1 # of Students 2 4 30 90 60 Class 3 90 5 4 # of Students 2 100 Scores 80 80 60 60 30 60
Ozone Ozone levels (in parts per billion, ppb) were recorded at sites in New Jersey monthly between 1926 and 1971. Here are boxplots of the data for each month (over the 46 years), lined up in order(January = 1):a) In what month was the highest ozone level ever recorded?b) Which month has the
Fuel economy 2012 The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of Combined Fuel Economy (using an average of driving conditions)in miles per gallon by vehicle Type (midsize car, standard pickup truck, or SUV) for 2012
Fuel economy by cylinders Describe what these boxplots tell you about the relationship between the number of cylinders a car’s engine has and the car’s fuel economy (mpg). 35 30 Fuel Efficiency 20 HIH 15 4 5 6 8 Cylinders
Marriage age In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show. Age at First Marriage 28 26 24 24 22 20 20 Women Men
Gas prices 2013 Here are boxplots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2009 through 2013.a) Compare the distribution of prices over the five years.b) Compare the stability of prices over the five years. 4.0 3.5 3.0
Women’s basketball Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra:a) Summarize the similarities and differences in their performance so far.b) The coach can take only one player to the state championship. Which one should she take?
Deaths 2011 A National Vital Statistics Report(www.cdc.govchs/) indicated that nearly 290,000 black Americans died in 2011, compared with just over 2 million white Americans. Below are histograms displaying the distributions of their ages at death.a) Describe the overall shapes of these
Hospital stays The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics. Data from a sample of 39 male patients and 35 female patients on length of stay(in days) are displayed in
Camp sites Shown below are the histogram and summary statistics for the number of camp sites at public parks in Vermont.a) Which statistics would you use to identify the center and spread of this distribution? Why?b) How many parks would you classify as outliers? Explain.c) Create a boxplot for
Population growth 2010 by region On the next page is a “back-to-back” stem-and-leaf display that shows two data sets at once—one going to the left, one to the right.The display compares the percent change in population for two regions of the United States (based on census figures for 2000 and
Tendon transfers People with spinal cord injuries may lose function in some, but not all, of their muscles.The ability to push oneself up is particularly important for shifting position when seated and for transferring into and out of wheelchairs. Surgeons compared two operations to restore the
Cereals Sugar is a major ingredient in many breakfast cereals. The histogram displays the sugar content as a percentage of weight for 49 brands of cereal. The boxplots compare sugar content for adult and children’s cereals.a) What is the range of the sugar contents of these cereals?b) Describe
Slalom times 2010 The Men’s Giant Slalom skiing event consists of two runs whose times are added together for a final score. Two displays of the giant slalom times in the 2010 Winter Olympics are shown below.a) What features of the distribution can you see in both the histogram and the boxplot?b)
Rock concert accidents Crowd Management Strategies(www.crowdsafe.com) monitors accidents at rock concerts.In their database, they list the names and other variables of victims whose deaths were attributed to“crowd crush” at rock concerts. Here are the histogram and boxplot of the victims’
Costs To help travelers know what to expect, researchers collected the prices of commodities in 16 cities throughout the world. Here are boxplots comparing the prices of a ride on public transportation, a newspaper, and a cup of coffee in the 16 cities (prices are all in US$).a) On average, which
Pizza prices by city A company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:a) Do prices
Groups on the Internet Find data on the Internet (or elsewhere) for two or more groups. Make appropriate displays to compare the groups, and interpret what you find.
Time on the Internet Find data on the Internet (or elsewhere)that give results recorded over time. Make an appropriate display and discuss what it shows.
In the news again Find an article in a newspaper, a magazine, or the Internet that shows a timeplot.a) Does the article discuss the W’s?b) Is the timeplot appropriate for the data? Explain.c) Discuss what the timeplot reveals about the variable.d) Does the article accurately describe and
In the news Find an article in a newspaper, a magazine, or the Internet that compares two or more groups of data.a) Does the article discuss the W’s?b) Is the chosen display appropriate? Explain.c) Discuss what the display reveals about the groups.d) Does the article accurately describe and
Exoplanets re-expressed Here are the exoplanet distances of Exercise 9, re-expressed to the log scale.a) Is this a better scale to understand these distances?b) The low outlier is “sol”– that is, it is the distance of the sun from the earth. Do you think it belongs with these data? 22 25 20
Exoplanets Discoveries of planets beyond our solar system have grown rapidly. Here is a histogram showing the distance (in light-years) from earth to stars having known planets (as of 2014).Explain why it might be beneficial to re-express these distances. 40 30 10 220 20 3000 Distance (ly) 0 1000
Load factors 2013 over time, a second look Here is a timeplot of the same domestic load factors as in Exercise 7, but this time with a different smoother (called a median smoother) applied.a) What patterns do you see in this plot?b) Do you expect the patterns you see here to continue for the next
Load factors 2013 over time Here is a timeplot of each monthly load factor for domestic flights for 2000 to 2013 along with a lowess smooth.a) Describe the patterns you see in this plot.b) Do you expect the overall pattern to continue for another decade? Why or why not? Domestic Load Factor (%) 55
Extraordinary months again Here’s a boxplot of all of the domestic load factors. It shows a single outlier.The boxplots of Exercise 4 show the same data, but have no outliers. Why do you think this is? Domestic Load Factor (%) 55
Extraordinary months Look at the boxplots by month in Exercise 3. The three outliers in September, October, and November are all from the year 2001 and reflect the terrorist attacks of 9/11. Do you think the data for these months should be set aside in any overall analysis of load factor patterns
Load factors 2013 by year Here is a display of the domestic load factors by year.Discuss the patterns you see in this display. Domestic Load Factor (%) 85 75 70 65 60 2000 '01 '02 '03 '04 '05 '06 '07 '08 '09 10 11 12 '13 Year
Load factors 2013 by month Here is a display of the international load factors by month for the period from 2000 to 2013.Discuss the patterns you see in this display. International Load Factor (%) 288 HOH HIH 1 2 3 4 HIH HIH H HIH HDH HIH 5 6 7 8 9 10 11 12 Month
Load factors, 2013 The Research and Innovative Technology Administration of the Bureau of Transportation Statistics (www.TranStats.bts.gov/Data_Elements.aspx?Data=2) reports load factors(passenger-miles as a percentage of available seat-miles)for commercial airlines for every month from 2000
Roller coaster1 riders want a coaster that goes fast. There are two main types of roller coasters: those with wooden tracks and those with steel tracks. Do they typically run at different speeds? Here are boxplots (Data in Coasters 2014):Question: Compare the speeds of wood and steel roller
The Nest Egg Index, devised by the investment firm of A.G. Edwards, is a measure of saving and investment performance for each of the 50 states, based on 12 economic factors, including participation in retirement savings plans, personal debt levels, and home ownership. The average index is 100 and
Prisons 2013 A report from the U.S. Department of Justice (www.ojp.usdoj.gov/bjs/) reported the percent changes in federal prison populations in 20 northeastern and midwestern states from 2000 to 2012. Using appropriate graphical displays and summary statistics, write a report on the changes in
Population growth 2010 The following data show the percentage change in population for the 50 states and the District of Columbia from the 2000 census to the 2010 census. Using appropriate graphical displays and summary statistics, write a report on the percentage change in population by state.
Boomtowns 2011 In 2011, the website NewGeography.com listed its ranking of the best cities for job growth in the United States. Here is the magazine’s top 20 larger cites, along with their weighted job rating index.a) Make a suitable display of the weighted growth indices.b) Summarize the typical
Math scores 2013 The National Center for Education Statistics (nces.ed.govationsreportcard/) reports average mathematics achievement scores for eighth graders in all 50 states:a) Find the median, the IQR, the mean, and the standard deviation of these state averages.b) Which summary statistics would
ZIP codes revisited Here are some summary statistics to go with the histogram of the ZIP codes of 500 customers from the Holes-R-Us Internet Jewelry Salon that we saw in Exercise 55What can these statistics tell you about the company’s sales? Count 500 Mean 64,970.0 StdDev 23,523.0 Median 64,871
ZIP codes Holes-R-Us, an Internet company that sells piercing jewelry, keeps transaction records on its sales. At a recent sales meeting, one of the staff presented a histogram of the ZIP codes of the last 500 customers, so that the staff might understand where sales are coming from. Comment on the
Final grades revisited After receiving many complaints about his final-grade histogram from students currently taking a Statistics course, the professor from Exercise 53 distributed the following revised histogram:a) Comment on this display.b) Describe the distribution of grades. 4321 # of Students
Final grades A professor (of something other than Statistics!)distributed the following histogram to show the distribution of grades on his 200-point final exam.Comment on the display. # of Students 50 40 30 20 10 60 50 100 150 200 Final Grade
Marijuana 2007 In 2007 the Council of Europe published a report entitled The European School Survey Project on Alcohol and Other Drugs (www.espad.org).Among other issues, the survey investigated the percentages of 16-year-olds who had used marijuana. Shown here are the results for 34 European
Acid rain Two researchers measured the pH (a scale on which a value of 7 is neutral and values below 7 are acidic) of water collected from rain and snow over a 6-month period in Allegheny County, Pennsylvania.Describe their data with a graph and a few sentences:4.57 5.62 4.12 5.29 4.64 4.31 4.30
Return of the birds 2013 Students were given the assignment to make a histogram of the data on bird counts reported in Exercise 46. One student submitted the following display:a) Comment on this graph.b) Create your own histogram of the data. # of Species 200 150 100 50 50 0 1 2 3 4 5 6 7 8 9 10 11
A-Rod again 2013 Students were asked to make a histogram of the number of home runs hit by Alex Rodriguez from 1994 to 2013 (see Exercise 45). One student submitted the following display (he noted that A Rod had hit no home runs in 1994):a) Comment on this graph.b) Create your own histogram of the
Horsepower Create a stem-and-leaf display for these horsepowers of autos reviewed by Consumer Reports, and describe the distribution: 155 103 130 80 65 142 125 129 71 69 125 115 138 68 78 150 133 135 135 90 97 68 105 88 115 110 95 85 109 115 71 97 110 65 90 75 120 80 70
Major Hurricanes 2013 The following data give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2013, as reported by NOAA (www.nhc.noaa.gov):3, 3, 1, 2, 4, 3, 8, 5, 3, 4, 2, 6, 2, 2, 5, 2, 2, 7, 1, 2, 6, 1, 3, 1, 0, 5, 2, 1, 0, 1, 2, 3, 2, 1,
Bird species 2013 The Cornell Lab of Ornithology holds an annual Christmas Bird Count (www.birdsource.org), in which bird watchers at various locations around the country see how many different species of birds they can spot. Here are the number of species counted from the 20 sites with the most
A-Rod 2013 Alex Rodriguez (known to fans as A-Rod)was the youngest player ever to hit 500 home runs. Here is a stem-and-leaf display of the number of home runs hit by A-Rod during the 1994–2013 seasons. (www.baseball-reference.com/players/r/rodrial01.shtml.) Describe the distribution, mentioning
Wayne Gretzky In Exercise 42, you examined the number of games played by hockey great Wayne Gretzky during his 20-year career in the NHL.a) Would you use the median or the mean to describe the center of this distribution? Why?b) Find the median.c) Without actually finding the mean, would you expect
States The stem-and-leaf display shows populations of the 50 states, in millions of people, according to the 2010 census.a) What measures of center and spread are most appropriate?b) Without doing any calculations, which must be larger:the median or the mean? Explain how you know.c) From the
The Great One During his 20 seasons in the NHL, Wayne Gretzky scored 50% more points than anyone who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder. Here are the number of games Gretzky played during
Gasoline A survey of 12 gas stations produced these prices for a gallon of regular gasoline:2.119 2.079 2.049 2.159 2.149 2.069 2.069 2.269 2.099 2.029 2.139 2.189a) Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 2.1 stems—one for prices between $2.10 and
Singers full choir The frequency table shows the heights(in inches) of 130 members of a choir.a) Find the median and IQR.b) Find the mean and standard deviation.c) Display these data with a histogram.d) Write a few sentences describing the distribution. Height Count 60 2 69 Height Count 6 61 62 63
Payroll A small warehouse employs a supervisor at$1000 a week, an inventory manager at $830 a week, six stock boys at $450 a week, and four drivers at $480 a week.a) Find the mean and median wage.b) How many employees earn more than the mean wage?c) Which measure of center best describes a typical
Cold weather A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures(in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the Celsius value of 2°. Assuming
Movie earnings 2013 The histogram shows total gross earnings (in millions of dollars) of the top 200 major release movies in 2013.An industry publication reports that the typical movie makes 29.6 million, but a watchdog group concerned with rising ticket prices says that the average earnings are
Golf drives II 2013 Exercise 34 looked at distances PGA golfers can hit the ball. The standard deviation of these average drive distances is 11.2 yards, and the quartiles are Q1 = 282.5 yards and Q3 = 295.6 yards.a) Write a sentence or two describing the spread in distances based on i) the
Movie lengths II 2010 Exercise 33 looked at the running times of movies released in 2010. The standard deviation of these running times is 16.6 minutes, and the quartiles are Q1 = 98 minutes and Q3 = 116 minutes.a) Write a sentence or two describing the spread in running times based on i) the
Golf drives 2013 The display shows the average drive distance (in yards) for 155 professional golfers during a week on the men’s PGA tour in 2013.a) Describe this distribution.b) Approximately what proportion of professional male golfers drive, on average, 280 yards or less?c) Estimate the mean
Movie lengths 2010 The histogram shows the running times in minutes of the 150 top-grossing feature films released in 2010.a) You plan to see a movie this weekend. Based on these movies, how long do you expect a typical movie to run?b) Would you be surprised to find that your movie ran for 2 12
Neck sizes again Look again at the histogram of men’s neck sizes in Exercise 30.a) Is the mean closer to 14, 15, or 16 inches? Why?b) Is the standard deviation closer to 1 inch, 3 inches, or 5 inches? Explain.
Pizza prices again Look again at the histogram of the pizza prices in Exercise 29.a) Is the mean closer to $2.40, $2.60, or $2.80? Why?b) Is the standard deviation closer to $0.15, $0.50, or$1.00? Explain.
Neck size The histogram shows the neck sizes (in inches)of 250 men recruited for a health study in Utah.Which summary statistics would you choose to summarize the center and spread in these data? Why? No. of Men 60 50 40 30 88 20 10 0 12 13 14 15 16 17 Neck Size (inches)
Pizza prices The histogram shows the distribution of the prices of plain pizza slices (in $) for 156 weeks in Dallas, TX.Which summary statistics would you choose to summarize the center and spread in these data? Why? 30 30 20 20 Frequency 10 10 0 2.2 2.4 2.6 Price 2.8 3.0
Standard deviation II For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding the standard deviations. Set 1 a) 4, 7, 7, 7, 10 b) 100, 140, 150, 160, 200 c)
Standard deviation I For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding the standard deviations. Set 1 a) 4, 7, 8, 9, 12 b) 10, 13, 14, 15, 18 c) 1, 6,
Sick days During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual “average” is 7 days of absence per employee. The union negotiators counter that the “average”employee misses only 3 days of work each year.Explain how both
Mistake A clerk entering salary data into a company spreadsheet accidentally put an extra “1” in the boss’s salary, listing it as $1,170,000 instead of $170,000.Explain how this error will affect these summary statistics for the company payroll:a) measures of center: median and mean.b)
Tornadoes Here are the annual numbers of deaths from tornadoes in a certain region:124 90 30 45 565 60 39 44 70 89 115 Find these statistics:a) meanb) median and quartilesc) range and IQR
Summaries Here are costs of ten electric smoothtop ranges rated very good or excellent by a consumer magazine.$ 1250 1400 1200 650 850 550 1150 950 650 900 Find these statistics:a) meanb) median and quartilesc) range and IQR
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