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elementary statistics

Questions and Answers of Elementary Statistics

[EX02-109] The following data are the yields (in pounds) of hops:3.9 3.4 5.1 2.7 4.4 7.0 5.6 2.6 4.8 5.6 7.0 4.8 5.0 6.8 4.8 3.7 5.8 3.6 4.0 5.6a. Find the first and the third quartiles of the
[EX02-108] Fifteen countries were randomly selected from the World Factbook 2004 list of world countries, and the infant mortality per 1000 live births rate was recorded:6.38 101.68 9.48 69.18 64.19
[EX02-107] The annual salaries (in $100)of the kindergarten and elementary school teachers employed at one of the elementary schools in the local school district are listed here:574 434 455 413 391
[EX02-106] Following are the American College Test (ACT) scores attained by the 25 members of a local high school graduating class:21 24 23 17 31 19 19 20 19 25 17 23 16 21 20 28 25 25 21 14 19 17 18
Refer to the table of exam scores in Table 2.16 on page 94 for the following.a. Using the concept of depth, describe the position of 91 in the set of 50 exam scores in two different ways.b. Find P20
Each of two samples has a standard deviation of 5. If the two sets of data are made into one set of 10 data, will the new sample have a standard deviation that is less than, about the same as, or
Start with x 100 and add four x values to make a sample of five data such that:a. s 0b. 0 s 1c. 5 s 10d. 20 s 30
Comment on the statement: “The mean loss for customers at First State Bank (which was not insured) was $150. The standard deviation of the losses was $125.”
[EX02-099] One measure of airline performance is about overall flight on-time rates. For January 2005, the on-time arrival rates of domestic flights at the 31 largest U.S. airports were as
[EX02-098] Better Roads magazine reported the percentage of interstate and state-owned bridges that were structurally deficient or functionally obsolete (%SD/FO) for each U.S. state in 2003.
[EX02-097] Recruits for a police academy were required to undergo a test that measures their exercise capacity. The exercise capacity (in minutes) was obtained for each of 20 recruits:25 27 30 33 30
[EX02-096] One aspect of the beauty of scenic landscape is its variability. The elevations (feet above sea level) of 12 randomly selected towns in the Finger Lakes Regions of Upstate New York are
Adding (or subtracting) the same number from each value in a set of data does not affect the measures of variability for that set of data.a. Find the variance of this set of annual heatingdegree-day
[EX02-071] A random sample of 10 of the 2005 Nextel Cup NASCAR drivers produced the following ages: 33, 48, 41, 29, 40, 48, 44, 42, 49, 28.a. Find the range.b. Find the variance.c. Find the standard
Fifteen randomly selected college students were asked to state the number of hours they slept the previous night. The resulting data are 5, 6, 6, 8, 7, 7, 9, 5, 4, 8, 11, 6, 7, 8, 7. Find the
Given the sample 7, 6, 10, 7, 5, 9, 3, 7, 5, 13, find the following:a. Variance s2 using formula (2.6)b. Variance s2, using formula (2.10)c. Standard deviation, s
Consider the sample 6, 8, 7, 5, 3, 7. Find the following:a. Rangeb. Variance s2, using formula (2.6)c. Standard deviation, s
Consider the sample 2, 4, 7, 8, 9. Find the following:a. Rangeb. Variance s2, using formula (2.6)c. Standard deviation, s
A sample contains the data {1, 3, 5, 6, 10}.a. Use formula (2.6) to find the variance.b. Use formula (2.10) to find the variance.c. Compare the results from parts a and b.
All measures of variation are nonnegative in value for all sets of data.a. What does it mean for a value to be “nonnegative”?b. Describe the conditions necessary for a measure of variation to
The summation (x x) is always zero.Why? Think back to the definition of the mean(p. 73) and see if you can justify this statement.
a. The data value x 45 has a deviation value of 12. Explain the meaning of this.b. The data value x 84 has a deviation value of 20. Explain the meaning of this.
In 2004 the Tax Policy Center reported the following statistics about the average annual 2002 taxes and percent of personal income paid per person by state.Taxes per Percent of Capita Rank Personal
Starting with the data values 70 and 100, add three data values to the sample so that the sample has the following: (Justify your answer in each case.)a. Mean of 100b. Median of 70c. Mode of 87d.
Your instructor and your class have made a deal on the exam just taken and currently being graded. If the class attains a mean score of 74 or better, there will be no homework on the coming weekend.
In what states do the residents pay the most taxes? the least? Perhaps it depends on the variable used to measure amount of taxes paid. In 2004 the Tax Policy Center reported the following statistics
You are responsible for planning the parking needed for a new 256-unit apartment complex, and you’re told to base the needs on the statistic“average number of vehicles per household is 1.9.”a.
[EX02-079] Students like to engage in the“Battle of the Sexes” when it comes to who’s the better driver. But which gender outnumbers the other on the road? The numbers may surprise you.Listed
[EX02-078] Does everything increase, every year? Sometimes it seems like it! The annual percentage rate of increase in motor-fuel consumption for 2002 to 2003 is listed in the following table by U.S.
[EX02-077] The number of runs scored by major league baseball (MLB) teams is likely influenced by whether the game is played at home or at the opponents’ ballpark. In an attempt to measure
[EX02-076] Consumers are frequently cautioned against eating too much food that is high in calories, fat, and sodium for numerous health and fitness reasons. Nutrition Action HealthLetter published a
[EX02-075] All the third-graders at Roth Elementary School were given a physical fitness strength test. These data resulted:12 22 6 9 2 9 5 9 3 5 16 1 22 18 6 12 21 23 9 10 24 21 17 11 18 19 17 5 14
The “average” is a commonly reported statistic.This single bit of information can be very informative or very misleading, with the mean and median being the two most commonly reported.a. The mean
[EX02-073] One measure of airline performance is overall flight on-time rates. For January 2005, the on-time arrival rates of domestic flights at the 31 largest U.S. airports were as follows.ATL
[EX02-072] A constant objective in the manufacture of contact lenses is to improve those features that affect lens power and visual acuity.One such feature involves the tooling from which lenses are
[EX02-071] A random sample of 10 of the 2005 Nextel Cup NASCAR drivers produced the following ages: 33, 48, 41, 29, 40, 48, 44, 42, 49, 28.a. Find the mean age for the 10 NASCAR drivers of the 2005
2.70 Fifteen randomly selected college students were asked to state the number of hours they slept the previous night. The resulting data values are 5, 6, 6, 8, 7, 7, 9, 5, 4, 8, 11, 6, 7, 8, 7. Find
2.69 Consider the sample 6, 8, 7, 5, 3, 7. Find the following:a. mean, ¯ xb. median, ˜ xc. moded. midrange
2.68 Consider the sample 2, 4, 7, 8, 9. Find the following:a. mean, ¯ xb. median, ˜ xc. moded. midrange
2.67a. Find the mean, median, mode, and midrange for the sample data 9, 6, 7, 9, 10, 8.b. Verify and discuss the relationship between the answers in parta, as shown in Figure 2.20 on page 77.
2.66 Each year, approximately 160 colleges compete in the National Concrete Canoe Competition.Each team must design a seaworthy canoe from a substance not known for its capacity to float. The canoes
2.65 The number of cars per apartment owned by a sample of tenants in a large complex is 1, 2, 1, 2, 2, 2, 1, 2, 3, 2. What is the mode?
2.63 Find the median rate paid at Jim’s Burgers if the workers’ hourly rates are $4.25, $4.15, $4.90,$4.25, $4.60, $4.50, $4.60, $4.75.
2.62 Find the median height of a basketball team:73, 76, 72, 70, and 74 inches.
2.61 Interstate 29 intersects many other highways as it crosses four states in Mid-America, stretching from the southern end in Kansas City, MO, at I-35 to the northern end in Pembina, ND, at the
2.60 U.S. Interstate 64 runs between Portsmouth, VA, at I-264 on the eastern end to St. Louis, MO, at I-270 on the western end. While passing through six states and five more major cities, I-64
2.58 The number of children, x, belonging to each of eight families registering for swimming was 1, 2, 1, 3, 2, 1, 5, 3. Find the mean, ¯ x.
2.57 Explain why it is possible to find the mean for the data of a quantitative variable but not for a qualitative variable.
2.55 [EX02-055] The Quality of Life in the Nation’s 100 Largest Cities and Their Suburbs: New and Continuing Challenges for Improving Health and Well-Being, June 2004, reports on the percent of
2.53 [EX02-041]a. Prepare a cumulative relative frequency distribution for the variable “KSW test score” in Exercise 2.41.b. Construct an ogive of the distribution.
2.52 [EX02-032]a. Prepare a cumulative relative frequency distribution for the variable “AP score” in Exercise 2.32.b. Construct an ogive of the distribution.
2.51 A survey of 100 resort club managers on their annual salaries resulted in the following frequency distribution. (See Exercise 2.39 on p. 69.)Annual Salary 15–25 25–35 35–45 45–55
2.49 Can you think of variables whose distribution might yield the following different shapes?(See Figure 2.13 on p. 63 if necessary.)a. A symmetrical, or normal, shapeb. A uniform shapec. A
2.48 [EX02-048] Education has long been considered the ticket for upward mobility in the United States. In today’s information age, a college education has become the minimum level of educational
2.47 [EX02-047] The Office of Coal, Nuclear, Electric and Alternate Fuels reported the following data as the costs (in cents) of the average revenue per kilowatt-hour for sectors in Arkansas:6.61
2.46 [EX02-046] People have marveled for years about the continuing eruptions of the geyser Old Faithful in Yellowstone National Park. The times of duration, in minutes, for a sample of 50 eruptions
2.45 [EX02-045] All of the third-graders at Roth Elementary School were given a physical-fitness strength test. The following data resulted:12 22 6 9 2 9 5 9 3 5 16 1 22 18 6 12 21 23 9 10 24 21 17
2.44 [EX02-044] The hemoglobin A1c test, a blood test given to diabetics patients during their periodic checkups, indicates the level of control of blood sugar during the past 2 to 3 months. The
2.43 [EX02-043] The speeds of 55 cars were measured by a radar device on a city street:27 23 22 38 43 24 35 26 28 18 20 25 23 22 52 31 30 41 45 29 27 43 29 28 27 25 29 28 24 37 28 29 18 26 33 25 27
2.42 [EX02-042] The USA Snapshot titled “Nuns an aging order” reports that the median age of the 94,022 Roman Catholic nuns in the United States is 65 years and the percentages of U.S. nuns by
2.41[EX02-041] The KSW computer science aptitude test was given to 50 students. The following frequency distribution resulted from their scores:KSW Test Score 0–4 4–8 8–12 12–16 16–20
2.37 [EX02-037] The opening-round scores for the Ladies’ Professional Golf Association tournament at Locust Hill Country Club were posted as follows:69 73 72 74 77 80 75 74 72 83 68 73 75 78 76 74
2.36 [EX02-036] Here are the ages of 50 dancers who responded to a call to audition for a musical comedy:21 19 22 19 18 20 23 19 19 20 19 20 21 22 21 20 22 20 21 20 21 19 21 21 19 19 20 19 19 19 20
2.35 [EX02-035] The 2003 American Community Survey universe is limited to the household population and excludes the population living in institutions, college dormitories, and other group quarters.
2.34 [EX02-034] The U.S. Census Bureau posted the following 2003 Report on America’s Families and Living Arrangements for all races.No. in Household Percentage No. in Household Percentage 1 26.4% 5
2.33 [EX02-033] The U.S. Women’s Olympic Soccer team had a great year in 2004. One way to describe the players on that team is by their individual heights.Height (inches)68 67 65 66 65 67 64 69 69
2.32 [EX02-032] The California Department of Education gives an annual report on the Advanced Placement (AP) test results for each year. In the 2003–2004 school year, Modoc County had students with
2.31 [EX02-031] The players on the Rochester Raging Rhinos professional soccer team scored 38 goals during the 2002 season.Player 1 2 3 4 5 6 7 8 9 10 11 12 13 Goals 2 8 1 2 2 6 2 1 5 2 3 2 2 Source:
2.30 Bar graphs and histograms are not the same thing. Explain their similarities and differences.
2.29a. Form an ungrouped frequency distribution of the following data:1, 2, 1, 0, 4, 2, 1, 1, 0, 1, 2, 4 Referring to the preceding distribution:b. Explain what f 5 represents.c. What is the sum of
2.28 A term often used in solar energy research is heating-degree-days. This concept is related to the difference between an indoor temperature of 65°F and the average outside temperature for a
2.27 Given the following stem-and-leaf display:Stem-and-Leaf of C1 N 16 Leaf Unit 0.010 1 59 7 4 60 148(5) 61 02669 7 62 0247 3 63 58 1 64 3a. What is the meaning of “Leaf Unit 0.010”?b.
2.26 [EX02-026] One of the many things the U.S.Census Bureau reports to the public is the increase in population for various geographic areas within the country. The percentages of increase in
2.23 [EX02-017] Construct a stem-and-leaf display of the number of points scored during each basketball game last season:56 54 61 71 46 61 55 68 60 66 54 61 52 36 64 51
2.19 [EX02-019] HoopsHype.com regularly posts the latest on the NBA. Following are the heights(in inches) of the basketball players who were the first round picks by the professional teams on June
2.18 [EX02-018] The table here lists the median house selling prices (in $1000s) for 20 U.S. cities as listed on Realtor.com.120 120 120 119 117 117 116 116 115 115 114 114 112 112 112 111 109 107
2.17 [EX02-017] The number of points scored during each game by a high school basketball team last season was as follows: 56, 54, 61, 71, 46, 61, 55, 68, 60, 66, 54, 61, 52, 36, 64, 51. Construct a
2.14 [EX02-014] The Office of Aviation Enforcement and Proceedings, U.S. Department of Transportation, posted this table listing the number of consumer complaints against top U.S. airlines by
2.13 [EX02-013] A study by Bruskin-Goldring for Whirlpool Corp. lists the major chores mothers say they would like to have the family help with.The most popular response was cleaning (53%), followed
2.10 Cleaning countertops, disinfecting surfaces, and personal hygiene are among consumers’ favorite uses for wipe products, according to The Soap and Detergent Association’s (SDA) latest
2.9 [EX02-009] The number of people, by age group, living in the 50 U.S. states and the District of Columbia in September 2004 was reported as follows.Number Number Age Group (millions) Age Group
2.8 [EX02-008] A sample of student-owned vehicles produced by General Motors was identified and the make of each noted. The resulting sample follows (Ch Chevrolet, P Pontiac, B Buick, O
2.7 The number of points scored by the winning teams on November 2, 2004, the opening night of the 2004–2005 NBA season, are listed here.Team Detroit Dallas LA Lakers Score 87 107 89 Source:
2.6 [EX02-006] The American Community Survey is limited to the household population and excludes the population living in institutions, college dormitories, and other group quarters. Montana’s 2003
Most people mentioned the importance of “comfort”in their explanations. The vast majority of respondents were very happy with their company’s dress code or policy.a. Construct a circle graph
American Payroll Association got a big response to this question about company dress code:“The current dress code at my company is . . .”Final results:a. A little too relaxed—27%b. A little too
How Americans prefer to eat an apple was reported in USA Today, November 11, 2004: Bite into it—47%, Cut it into slices—39%, Peel—11%, Don’t Know—3%.a. Construct a circle graph showing how
As a statistical graph the circle graph has limitations.Examine the circle graph in Figure 2.1 and the bar graph in Figure 2.2.a. What information do they both demonstrate?b. What information is
a. How many different Internet activities did you engage in last week?b. How do you think you compare to the 40 Internet users in the sample in Exercise 2.1?c. How do you think you compare to all
Students in an online statistics course were asked how many different Internet activities they engaged in during a typical week. The following data show the number of activities:6 7 3 6 9 10 8 9 9 6
1.16 What conditions are required for a sample to be a random sample? Explain and include an example of a sample that is random and one that is not random.
1.15 The data, the statistic, and the parameter are all values used to describe a statistical situation.How does one distinguish among these three terms? Give an example.
1.14 The variable and the data for a specific situation are closely related. Explain this relationship and give an example.
1.13 The population and the sample are both sets of objects. Describe the relationship between them and give an example.
1.11 Classify each of the following variables as nominal, ordinal, discrete, or continuous:a. Method of payment for purchases (cash, credit card, check)b. Customer satisfaction (very satisfied,
1.89 Select one of the “Americans, Here’s Looking at You” graphics (p. 1); then, using the students at your school or college as the population of concern, collect sample data from 30 students
1.88 With respect to the four graphics in Section 1.1 on pages 1 and 2, complete the following:a. What statistical population is of concern for all of these graphics?b. Identify one specific graphic.
1.87 In Exercise 1.5, you were asked to write a sentence for each of the three statistical activities given in the definition of statisitics. Now that you have completed the chapter, review your
1.86a. Find an article in a newspaper or magazine that exemplifies the use of statistics in a way that might be considered “entertainment”or “recreational.” Describe why you think this
1.85 Find an article or an advertisement in a newspaper or magazine that exemplifies the use of statistics.a. Identify and describe one statistic reported in the article.b. Identify and describe the

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