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Statistics The Art And Science Of Learning From Data 3rd Edition Alan Agresti, Christine A. Franklin - Solutions

How do cigarette taxes per pack vary from one state to the next? The data set of 2003 cigarette taxes for all 50 states and Washington, D.C. is in the Cigarette Tax data file on the text CD. a. Use software to construct a histogram. Write a short description of the distribution, noting shape and
Revisit the sugar data for breakfast cereals that are given in the table.a. Interpret the box plot in the figure (MINITAB output) by giving approximate values for the five-number summary.b. What does the box of the box plot suggest about possible skew?c. The mean is 8.75 and the standard deviation
The data values below represent the prices per share of the 20 most actively traded stocks on the New York Stock Exchange (rounded to the nearest dollar) on February 18, 2011.a. Sketch a dot plot or construct a stem-and-leaf plot.b. Find the median, the first quartile, and the third quartile.c.
Access the Central Park temps data file on the text CD.a. Using software, construct a histogram of average March temperatures and interpret, noting shape, center, and variability.b. Find and interpret the mean and standard deviation of March temperatures.c. Construct a histogram of average November
According to Statistical Abstract of the United States, 2006, average salary (in dollars) of secondary school classroom teachers in 2004 in the United States varied among states with a five-number summary of: minimum = 33,100, Q1 = 39,250, Median = 42,700, Q3 = 48,850, Maximum = 61,800. a. Find and
In 2004, the five-number summary of positions for the distribution of statewide percentage of people without health insurance had a minimum of 8.9% (Minnesota), Q1 = 11.6, Median = 14.2, Q3 = 17.0, and maximum of 25.0% (Texas) (Statistical Abstract of the United States, 2006). a. Do you think the
Which countries are most frequently visited by tourists from other countries? The table shows results according to Travel and Leisure magazine (2005). a. Is country visited a categorical or a quantitative variable? b. In creating a bar graph of these data, would it be most sensible to list the
For each of the following variables, sketch a box plot that would be plausible. a. Exam score (min = 0 max = 100, mean = 87, standard deviation = 10) b. IQ mean = 100 and standard deviation = 16 c. Weekly religious contribution median = $10 and mean = $17)
The distribution of high school graduation rates in the United States in 2004 had a minimum value of 78.3 (Texas), first quartile of 83.6, median of 87.2, third quartile of 88.8, and maximum value of 92.3 (Minnesota) (Statistical Abstract of the United States, 2006). a. Report the range and the
The U.S. statewide average total SAT scores math + reading + writing for 2010 are summarized in the box plot. These SAT scores are out of a possible 2400.a. Explain how the box plot gives you information about the distribution shape. b. Using the box plot, give the approximate value for each
A World Health Organization study (the MONICA project) of health in various countries reported that in Canada, systolic blood pressure readings have a mean of 121 and a standard deviation of 16. A reading above 140 is considered to be high blood pressure. a. What is the z -score for a blood
The cereal sodium values have a mean of 167 and a standard deviation of 77.3. Find the z -score for the cereal that has a sodium value of 0. Interpret.
Roger Maris, who spent most of his professional baseball career with the New York Yankees, held the record for the most home runs in one season (61) from 1961 until 1998, when the record was broken by Mark McGwire. Maris played in the major leagues from 1957 to 1968. The number of home runs he hit
A study of 13 children suffering from asthma (Clinical and Experimental Allergy, vol. 20, pp. 429€“432, 1990) compared single inhaled doses of formoterol (F) and salbutamol (S). Each child was evaluated using both medications. The outcome measured was the child€™s peak
Table 2.1, part of which is shown again below, summarized shark attacks for different regions of the world. Using software or sketching, construct a bar graph, ordering the regions (i) alphabetically, and (ii) as in a Pareto chart. Which do you prefer? Why? Region
To compare two groups graphically, one can use the same stems for each and put leaves for one group on one side and for the other group on the other side. This is called a back-to back stem-and-leaf plot. The figure shown compares sugar amounts (expressed in milligrams) for cereals listed in the
Give an example of a variable that you’d expect to have a distribution that isa. Approximately symmetricb. Skewed to the rightc. Skewed to the leftd. Bimodale. Skewed to the right, with a mode and median of 0 but a positive mean
Where do Americans tend to fall on the conservative€“liberal political spectrum? The General Social Survey asks, €œI€™m going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal, point 1, to extremely
The previous exercise showed how to find the mean and median when a categorical variable has ordered categories. A categorical scale that does not have ordered categories (such as choice of religious affiliation or choice of major in college) is called a nominal scale. For such a variable, the mode
a. The mean, median, and mode can never all be the same. b. The mean is always one of the data points. c. When n is odd, the median is one of the data points. d. The median is the same as the second quartile and the 50th percentile.
For the breakfast cereal data given in Table 2.3, a dot plot for the sugar values (in grams) is shown:a. Identify the minimum and maximum sugar values.b. Which sugar outcomes occur most frequently? What are these values called?
Refer to the calculation of the mean in Example 12 or in Exercise 2.133. Explain why the mean for grouped data can be expressed as a sum, taking each possible outcome times the proportion of times it occurred.
According to a recent report from the U.S. National Center for Health Statistics, for males aged 25–34 years, 2% of their heights are 64 inches or less, 8% are 66 inches or less, 27% are 68 inches or less, 39% are 69 inches or less, 54% are 70 inches or less, 68% are 71 inches or less, 80% are 72
Use the empirical rule to explain why the standard deviation of a bell-shaped distribution for a large data set is often roughly related to the range by evaluating Range ≈ 6s. (For small data sets, one may not get any extremely large or small observations, and the range may be smaller, for
We’ve seen that measures such as the mean, the range, and the standard deviation can be highly influenced by outliers. Explain why the range is worst in this sense.
The standard deviation is the most popular measure of variability from the mean. It uses squared deviations, since the ordinary deviations sum to zero. An alternative measure is the mean absolute deviation, ∑| x - |/n. a. Explain why greater variability tends to result in larger values of this
The mean and standard deviation of a sample may change if data are rescaled (for instance, temperature changed from Fahrenheit to Celsius). For a sample with mean, adding a constant c to each observation changes the mean to + c, and the standard deviation s is unchanged. Multiplying each
Access the General Social Survey at sda.berkeley.edu/GSS.a. Find the frequency table and histogram for Example 6 on TV watching.b. Your instructor will have you obtain graphical and numerical summaries for another variable from the GSS. Students will compare results in class.
Stub Hub is a popular Web site where fans can buy and sell tickets to concerts and sporting events. Below are data representing the amounts (in dollars) that buyers using StubHub spent on Super Bowl XLV tickets?a. Construct a stem-and-leaf plot. Truncate the data to the first two digits for
A teacher shows her class the scores on the midterm exam in the stem-and-leaf plot shown:6 588a. Identify the number of students and their minimum and maximum scores. b. Sketch how the data could be displayed in a dot plot. c. Sketch how the data could be displayed in a histogram with four
The fertility rate for a nation is the average number of children per adult woman. The table below part c shows results for western European nations, the United States, Canada, and Mexico, as reported by the United Nations in 2005.a. Construct a stem-and-leaf plot using stems 1 and 2 and the
For the fertility data in the previous exercise, MINITAB reports the stem-and-leaf plot shown below. (You can ignore the cumulative counts in the left column if your instructor has not explained this feature of a MINITAB stem-and-leaf plot.)a. Explain how this plot was formed using the data in the
When the observations are large numbers, their final digits are not shown in a stem-and-leaf plot. The plot specifies a leaf unit by which to multiply each observation. For instance, for the cereal sugar data from Table 2.3 expressed in milligrams (an excerpt of which is shown), MINITAB software
The figure below shows the stem-and-leaf plot for the cereal sodium values constructed after Example 5 using split stems, with leaves from 0 to 4 on the first split stem and leaves from 5 to 9 on the second.a. Explain why the truncated data shown here go from 0 to 34. b. Identify on the plot the
For the breakfast cereal data, the figure at the top of next column shows a histogram (constructed using MINITAB) for the sugar values, in grams.a. Identify the intervals of sugar values used for the plot.b. Describe the shape of the distribution. What do you think might account for this unusual
Using software with the Cereal data set on the text CD, construct (a) A dot plot. (b) A stemand- leaf plot. (c) A histogram. Explain how to interpret each plot.
For each of the following variables, indicate whether you would expect its histogram to be symmetric, skewed to the right, or skewed to the left. Explain why. a. Assessed value of houses in a large city b. Number of times checking account overdrawn in the past year for the faculty in your school c.
Repeat the preceding exercise for a. The scores of researchers (out of 100 points) on a very easy exam in which most score perfectly or nearly so, but a few score very poorly b. The weekly church contribution for all members of a congregation, in which the three wealthiest members contribute
Question 14 on the class survey (Activity 3 in Chapter 1 on pages 22€“23) asked, €œEstimate the number of times a week, on average, that you read a daily newspaper.€a. Is this variable continuous, or discrete? Explain.b. The histogram shown gives results of this
A data set analyzed by the famous statistician R. A. Fisher consisted of measurements of different varieties of iris blossoms. Below is a histogram representing the widths of the petals of Iris setosa.a. Describe the shape of the distribution of setosa petal widths. b. Of the 50 setosa blossoms in
The first figure shows a histogram of the Central Park, New York, annual average temperatures from 1869€“2010.a. Describe the shape of the distribution. b. What information can the time plot above show that a histogram cannot provide? c. What information does the histogram show that a
In the first half of the 20th century, whooping cough was a frequently occurring bacterial infection that often resulted in death, especially among young children. A vaccination for whooping cough was developed in the 1940s. How effective has the vaccination been in eradicating whooping cough? One
Access the Newnan, GA Temps file on the text CD, which reports the average annual temperatures during the 20th century for Newnan, Georgia. Construct a time plot to investigate a possible trend over time. Is there evidence of climate change?
Identify each of the following variables as categorical or quantitative. a. Number of pets in family b. County of residence c. Choice of auto to buy (domestic or import) d. Distance (in kilometers) of commute to work
The mean and median describe the center. a. Why is the median sometimes preferred? Give an example. b. Why is the mean sometimes preferred? Give an example.
The Energy Information Agency reported the CO2 emissions from fossil fuel combustion for the seven countries in 2008 with the highest emissions. These values, reported as million metric tons of carbon equivalent, are 6534 (China), 5833 (United States), 1729 (Russia), 1495 (India), 1214 (Japan), 829
Consider the following three sets of observations:Set 1: 8, 9, 10, 11, 12Set 2: 8, 9, 10, 11, 100Set 3: 8, 9, 10, 11, 1000a. Find the median for each data set.b. Find the mean for each data set.c. What do these data sets illustrate about the resistance of the median and mean?
The workers and the management of a company are having a labor dispute. Explain why the workers might use the median income of all the employees to justify a raise but management might use the mean income to argue that a raise is not needed.
The figure shows dot plots for three sample data sets.a. For which, if any, data sets would you expect the mean and the median to be the same? Explain why.b. For which, if any, data sets would you expect the mean and the median to differ? Which would be larger, the mean or the median? Why?
The owner of a company in downtown Atlanta is concerned about the large use of gasoline by her employees due to urban sprawl, traffic congestion, and the use of energy inefficient vehicles such as SUVs. She’d like to promote the use of public transportation. She decides to investigate how many
Refer to the previous exercise. a. Use the Mean Versus Median applet to investigate what effect adding the outlier of 90 to the data set has on the mean and median. b. Now add 10 more data values that are near the mean of 2 for the original 10 observations. Does the outlier of 90 still have such a
If you had data for all students in your school on the amount of money spent in the previous year on overnight stays in a hospital, probably the median and mode would be 0 but the mean would be positive. a. Explain why. b. Give an example of another variable that would have this property.
Identify each of the following variables as either categorical or quantitative. a. Choice of diet (vegetarian, non-vegetarian) b. Time spent in previous month attending a place of religious worship c. Ownership of a personal computer (yes, no) d. Number of people you have known who have been
The Statistical Abstract of the United States reported that in 2004 for those with a college education, the median net worth was $226,100 and the mean net worth was $851,300. For those with a high school diploma only, the values were $68,700 and $196,800. a. Explain how the mean and median could be
The players on the New York Yankees baseball team in 2010 had a mean salary of $7,935,531 and a median salary of $4,525,000 .7 what do you think causes these two values to be so different?
The European fertility rates (mean number of children per adult woman) from Exercise 2.17 are shown again in the table.a. Find the median of the fertility rates. Interpret.b. Find the mean of the fertility rates. Interpret.c. For each woman, the number of children is a whole number, such as 2 or 3.
A recent General Social Survey asked female respondents, “How many sex partners have you had in the last 12 months?” Of the 365 respondents, 102 said 0 partners, 233 said 1 partner, 18 said 2 partners, 9 said 3 partners, 2 said 4 partners, and 1 said 5 partners. (Source: Data from CSM, UC
The table summarizes responses of 4383 subjects in a recent General Social Survey to the question, “Within the past month, how many people have you known personally that were victims of homicide?” Number of People You Have Known Who Were Victims of Homicide Number of Victims
One variable in a study measures how many serious motor vehicle accidents a subject has had in the past year. Explain why the mean would likely be more useful than the median for summarizing the responses of the 60 subjects.
A company decides to investigate the amount of sick leave taken by its employees. A sample of eight employees yields the following numbers of days of sick leave taken in the past year:0 0 4 0 0 0 6 0a. Find and interpret the range.b. Find and interpret the standard deviation s.c. Suppose the 6 was
The Human Development Report 2006, published by the United Nations, showed life expectancies by country. For Western Europe, the values reported wereDenmark 77, Portugal 77, Netherlands 78, Finland 78,Greece 78, Ireland 78, UK 78, Belgium 79, France 79,Germany 79, Norway 79, Italy 80, Spain 80,
a. Explain the difference between a discrete variable and a continuous variable. b. Give an example of each type.
According to the National Association of Home Builders, the median selling price of new homes in the United States in January 2007 was $239,800. Which of the following is the most plausible value for the standard deviation: - + 15,000, + 1000, + 60,000, or + 1,000,000? Why? Explain what’s
For an exam given to a class, the students’ scores ranged from 35 to 98, with a mean of 74. Which of the following is the most realistic value for the standard deviation: -10, 0, 3, 12, 63? Clearly explain what’s unrealistic about each of the other values.
For the sample heights of Georgia college students in Example 15, the males had = 71 and s = 3 and the females had = 65 and s = 3. a. Use the empirical rule to describe the distribution of heights for males. b. The standard deviation for the overall distribution (combining females and males)
The figure shows histograms for three different samples, each with sample size n = 100.a. Which sample has the (i) largest and (ii) smallest standard deviation?b. To which sample(s) is the empirical rule relevant? Why?
The High School Female Athletes data file on the text CD has data for 57 female high school athletes on the maximum number of pounds they were able to bench press. The data are roughly bell shaped, with = 79.9 and s = 13.3. Use the empirical rule to describe the distribution.
The College Athletes data file on the text CD has data for 64 female college athletes. The data on weight (in pounds) are roughly bell shaped with = 133 and s = 17. a. Give an interval within which about 95% of the weights fall. b. Identify the weight of an athlete who is three standard
A recent summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C. in the United States reported = 73 and s = 48. Based on these values, do you think that this distribution is bell shaped? If so, why? If not, why not, and what shape would you expect?
Example 12 gave data on the number of times married. For the observations for men, shown below, = 0.16 and s = 0.37.a. Find the actual percentages of observations within 1, 2, and 3 standard deviations of the mean. How do these compare to the percentages predicted by the empirical rule? b. How do
The 2008 General Social Survey asked, “On the average day, about how many hours do you personally watch television?” Of 1,324 responses, the mode was 2, the median was 2, the mean was 2.98, and the standard deviation was 2.66. Based on these statistics, what would you surmise about the shape of
A recent General Social Survey asked respondents how many close friends they had. For a sample of 1467 people, the mean was 7.4 and the standard deviation was 11.0. The distribution had a median of 5 and a mode of 4. a. Based on these statistics, what would you surmise about the shape of the
Identify each of the following variables as continuous or discrete. a. The length of time to run a marathon b. The number of people in line at a box office to purchase theater tickets c. The weight of a dog d. The number of people you have dated in the past month
If the largest observation is less than 1 standard deviation above the mean, then the distribution tends to be skewed to the left. If the smallest observation is less than 1 standard deviation below the mean, then the distribution tends to be skewed to the right. A professor examined the results of
The European Union Unemployment data file on the text CD contains unemployment rates in December 2003 for the 25 countries that were in the European Union in 2004. Using software, a. Construct a graph to describe these values. b. Find the standard deviation. Interpret.
Use the Standard Deviation applet on the text CD to investigate how the standard deviation changes as the data change. a. Create 10 observations that have a mean of 5 and a standard deviation of about 2. b. Create 10 observations that have a mean of 5 and a standard deviation of about 4. c. Placing
National Geographic Traveler magazine recently presented data on the annual number of vacation days averaged by residents of eight different countries. They reported 42 days for Italy, 37 for France, 35 for Germany, 34 for Brazil, 28 for Britain, 26 for Canada, 25 for Japan, and 13 for the United
In recent years, many European nations have suffered from relatively high unemployment. For the 15 nations that made up the European Union in 2003, the table shows the unemployment rates reported by Eurostat as of January 2007.a. Find and interpret the median.b. Find the first quartile (Q1) and the
The High School Female Athletes data file on the text CD has data for 57 high school female athletes on the maximum number of pounds they were able to bench press, which is a measure of strength. For these data, = 79.9, Q1 = 70, median = 80, Q3 = 90. a. Interpret the quartiles. b. Would you guess
The College Athletes data file on the text CD has data for 64 college female athletes. The data on weight (in pounds) has = 133, Q1 = 119, median = 131.5, Q3 = 144. a. Interpret the quartiles. b. Would you guess that the distribution is skewed, or roughly symmetric? Why?
The standard deviation, the range, and the interquartile range (IQR) summarize the variability of the data. a. Why is the standard deviation s usually preferred over the range? b. Why is the IQR sometimes preferred to s? c. What is an advantage of s over the IQR?
Here’s the five-number summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C. in the United States. Minimum = 2.5, Q1 = 36, Median = 60, Q3 = 100, Maximum = 205 a. About what proportion of the states have cigarette taxes (i) greater than 36 cents and
Exercise 2.47 showed data for a company that investigated the annual number of days of sick leave taken by its employees. The data area. The standard deviation is 2.4. Find and interpret the range. b. The quartiles are Q1 = 0, median = 0, Q3 = 2. Find the interquartile range. c. Suppose the 6 was
Repeat the previous exercise for the following: a. The total playing time of a CD b. The number of courses for which a student has received credit c. The amount of money in your pocket d. The distance between where you live and your statistics classroom, when you measure it precisely with values
The Human Development Report 2006 published by the United Nations, showed infant mortality rates (number of infant deaths per 1000 live births) by country. For Africa, some of the values reported were: South Africa 54, Sudan 63, Ghana 68, Madagascar 76, Senegal 78, Zimbabwe 79, Uganda 80, Congo 81,
For Western Europe, the infant mortality rates reported by the Human Development Report 2006 were Sweden 3, Finland 3, Spain 3, Belgium 4, Denmark 4, France 4, Germany 4, Greece 4, Italy 4, Norway 4, Portugal 4, Netherlands 5, Switzerland 5, UK 5. Show that Q1 = Q2 = Q3 = 4. (The quartiles, like
During a recent semester at the University of Florida, students having accounts on a mainframe computer had storage space use (in kilobytes) described by the five-number summary, minimum = 4, Q1 = 256, median = 530, Q3 = 1105, and maximum = 320,000. a. Would you expect this distribution to be
Exercise 2.27 showed a histogram for the distribution of Central Park annual average temperatures for the 20th century. The box plot for these data is shown here.a. If this distribution is skewed, would you expect it to be skewed to the right or to the left? Explain. b. Approximate each component
The scores on an exam have mean = 88, standard deviation = 10, minimum = 65, Q1 = 77, median = 85, Q3 = 91, maximum = 100. Sketch a box plot, labeling which of these values are used in the plot.
Exercise 2.37 described a survey about how many miles per day employees of a company use public transportation. The sample values were 0 0 4 0 0 0 10 0 6 0 a. Identify the five-number summary, and sketch a box plot. b. Explain why Q1 and the median share the same line in the box. c. Why does the
The Energy Information Administration records per capita consumption of energy by country. The 2006 data for the 27 nations that now make up the European Union are used to create the boxplot below. The energy values (in millions of BTUs) have a mean of 167.8 and a standard deviation of 72.8, and
The 2007 unemployment rates of countries in the European Union shown in Exercise 2.64 ranged from 3.2 to 8.7, with Q1 = 4.5, median = 6.7, Q3 = 7.8, a mean of 6.3, and standard deviation of 1.8.a. In a box plot, what would be the values at the outer edges of the box, and what would be the values to
Example 18 discussed EU carbon dioxide emissions, which had a mean of 8.3 and standard deviation of 3.6.a. Canada’s observation was 16.5. Find its z -score relative to the distribution of values for the EU nations, and interpret.b. Sweden’s observation was 5.0. Find its z -score, and interpret.
For the 261 female heights shown in the box plot in Figure 2.16, the mean was 65.3 inches and the standard deviation was 3.0 inches. The shortest person in this sample had a height of 56 inches.a. Find the z -score for the height of 56 inches.b. What does the negative sign for the z –score
In the 2008 General Social Survey, 2020 respondents answered the question, €œHow many children have you ever had?€ The results werea. Is the variable, number of children, categorical or quantitative? b. Is the variable, number of children, discrete or continuous? c. Add
The manager of a fast-food restaurant records each day for a year the amount of money received from sales of food that day. Using software, he finds a bell shaped histogram with a mean of $1165 and a standard deviation of $220. Today the sales equaled $2000. Is this an unusually good day? Answer by
Refer to the FL Student Survey data set on the text CD and the data on weekly hours of TV watching. a. Use software to construct a box plot. Interpret the information on the plot, and use it to describe the shape of the distribution. b. Using a criterion for outliers, investigate whether there are
Refer to the previous exercise. Suppose you wanted to compare TV watching of males and females. Construct a side-by-side box plot to do this. Interpret.
The MINITAB vertical side-by-side box plots shown below compare the values reported by the UN of per capita carbon dioxide emissions for nations in the European Union and in South America, in 2003.a. Give the approximate value of carbon dioxide emissions for the outlier shown.b. What shape would
The six full-time employees of Linda’s Tanning Salon near campus had annual incomes last year of $8900, $9200, $9200, $9300, $9500, $9800. Linda herself made $250,000. a. For the seven annual incomes at Linda’s Salon, report the mean and median. b. Why is it misleading for Linda to boast to her

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