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mathematics
statistics

Elementary Statistics A Step By Step Approach 8th Edition Allan Bluman - Solutions

A random sample of bonuses (in millions of dollars) paid by large companies to their executives is shown. These data will be used for Exercise 18 in Section 3–2.Class boundaries
The hourly compensation costs (in U.S. dollars) for production workers in selected countries are represented below.Class Frequency2.48–7.48.....77.49–12.49......312.50–17.50....117.51–22.51....722.52–27.52....527.53–32.53....5Compare the mean of these grouped data to the U.S. mean of
Thirty automobiles were tested for fuel efficiency (in miles per gallon). This frequency distribution was obtained. (The data in this exercise will be used in Exercise 20 in Section 3–2.)Class boundaries Frequency7.5–12.5
The percentage of foreign-born population for each of the 50 states is represented below. Do you think the mean is the best average for this set of data? Explain. Percentage Frequency 0.8–4.4
Find the mean and modal class for each set of data in Exercises 8 and 18 in Section 2–2. Is the average about the same for both sets of data? Find the : Mean Modal class
Below are the percentages of the population over 25 years of age who have completed 4 years of college or more for the 50 states and the District of Columbia. Find the mean and modal class. Percentage Frequency 15.2–19.6 .......3 19.7–24.1........15 24.2–28.6........19
These data represent the net worth (in millions of dollars) of 45 national corporations.Class limits Frequency10–20 221–31 832–42 1543–53 754–64 1065–75 3Find the :MeanModal class
A random sample of 30 states shows the number of specialty coffee shops for a specific company.Class boundaries Frequency0.5–19.5 1219.5–38.5 738.5–57.5 557.5–76.5 376.5–95.5 3Find the :MeanModal class
The number of short-term parking spaces at 15 airports is shown.
This frequency distribution represents the commission earned (in dollars) by 100 salespeople employed at several branches of a large chain store. Class limits Frequency 150–158 .......5 159–167 ......16 168–176 ......20 177–185 ......21 186–194 ......20 195–203 ......15 204–212
This frequency distribution represents the data obtained from a sample of 75 copying machine service technicians. The values represent the days between service calls for various copying machines. Class boundaries Frequency 15.5–18.5 ......14 18.5–21.5 ......12 21.5–24.5 ......18 24.5–27.5
Use the data from Exercise 14 in Section 2–1 and find the mean and modal class.
Find the mean and modal class for the data in Exercise 13 in Section 2–1.
Use the data from Exercise 3 in Section 2–2 and find the mean and modal class.
Listed below are the enrollments for selected independent religiously controlled 4-year colleges that offer bachelor€™s degrees only. Construct a grouped frequency distribution with six classes and find the mean and modal class.
Find the weighted mean price of three models of automobiles sold. The number and price of each model sold are shown in this list.
Using the weighted mean, find the average number of grams of fat per ounce of meat or fish that a person would consume over a 5-day period if he ate these: Meat or fish Fat (g/oz) 3 oz fried shrimp 3.33 3 oz veal cutlet (broiled) 3.00 2 oz roast beef (lean) 2.50 2.5 oz
A recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
The costs of three models of helicopters are shown here. Find the weighted mean of the costs of the models.
The reported high temperatures (in degrees Fahrenheit) for selected world cities on an October day are shown below. Which measure of central tendency do you think best describes these data?
An instructor grades exams, 20%; term paper, 30%; final exam, 50%. A student had grades of 83, 72, and 90, respectively, for exams, term paper, and final exam. Find the student’s final average. Use the weighted mean.
Another instructor gives four 1-hour exams and one final exam, which counts as two 1-hour exams. Find a student’s grade if she received 62, 83, 97, and 90 on the 1-hour exams and 82 on the final exam.
For these situations, state which measure of central tendency—mean, median, or mode—should be used. a. The most typical case is desired. Mode b. The distribution is open-ended. Median c. There is an extreme value in the data set. Median d. The data are categorical. Mode e. Further statistical
Describe which measure of central tendency—mean, median, or mode—was probably used in each situation. a. One-half of the factory workers make more than $5.37 per hour, and one-half make less than $5.37 per hour. b. The average number of children per family in the Plaza Heights Complex is 1.8.
If the mean of five values is 8.2 and four of the values are 6, 10, 7, and 12, find the fifth value.
Find the mean of 10, 20, 30, 40, and 50.a. Add 10 to each value and find the mean.b. Subtract 10 from each value and find the mean.c. Multiply each value by 10 and find the mean.d. Divide each value by 10 and find the mean.e. Make a general statement about each
The harmonic mean (HM) is defined as the number of values divided by the sum of the reciprocals of each value. The formula isFor example, the harmonic mean of 1, 4, 5, and 2 isThis mean is useful for finding the average speed. Suppose a person drove 100 miles at 40 miles per hour and returned
The number of observers in the Frogwatch USA program (a wildlife conservation program dedicated to helping conserve frogs and toads) for the top 10 states with the most observers is 484, 483, 422, 396, 378, 352, 338, 331, 318, and 302. The top 10 states with the most active watchers list these
The geometric mean (GM) is defined as the nth root of the product of n values. The formula isGM = n √(X1) (X2) (X3). (Xn)The geometric mean of 4 and 16 isGM = √ (4) (16) = √64 = 8The geometric mean of 1, 3, and 9 isGM = 3√ (1)(3)(9) = 3√ 27 = 3The geometric mean is useful in finding the
A useful mean in the physical sciences (such as voltage) is the quadratic mean (QM), which is found by taking the square root of the average of the squares of each value. The formula isThe quadratic mean of 3, 5, 6, and 10 is Find the quadratic mean of 8, 6, 3, 5, and 4.
An approximate median can be found for data that have been grouped into a frequency distribution. First it is necessary to find the median class. This is the class that contains the median value. That is the n / 2 data value. Then it is assumed that the data values are evenly distributed throughout
The expenditures per pupil for selected states are listed below. Based on these data, what do you think of the claim that the average expenditure per pupil in the United States exceeds $10,000?Finda. Meanb. Medianc. Moded. Midrange
Forbes magazine prints an annual Top-Earning Nonliving Celebrities list (based on royalties and estate earnings). Find the measures of central tendency for these data and comment on the skewness. Figures represent millions of dollars.Kurt Cobain 50 Ray Charles 10Elvis Presley 42 Marilyn Monroe
Twelve major earthquakes had Richter magnitudes shown here.7.0, 6.2, 7.7, 8.0, 6.4, 6.2,7.2, 5.4, 6.4, 6.5, 7.2, 5.4
The data shown are the total compensation (in millions of dollars) for the 50 top-paid CEOs for a recent year. Compare the averages, and state which one you think is the best measure. Find the a. Meanb. Medianc. Moded. Midrange
The amount of garbage in millions of tons collected over a 16-year period is shown.Find the a. Meanb. Medianc. Moded. Midrange
The total surface area (in square miles) for each of six selected Eastern states is listed here.28,995 PA 37,534 FL31,361NY 27,087 VA20,966 ME 37,741 GAThe total surface area for each of six selected Western states is listed (in square miles).72,964 AZ 70,763 NV101,510 CA 62,161 OR66,625 CO 54,339
The number of stories in the 13 tallest buildings for two different cities is listed below. Which set of data is more variable?Houston: 75, 71, 64, 56, 53, 55, 47, 55, 52, 50, 50, 50, 47Pittsburgh: 64, 54, 40, 32, 46, 44, 42, 41, 40, 40, 34, 32, 30Find the range, variance, and standard deviation
Starting teachers’ salaries (in equivalent U.S. dollars) for upper secondary education in selected countries are listed below. Which set of data is more variable? (The U.S. average starting salary at this time was $29,641.)Europe AsiaSweden $48,704 Korea $26,852Germany 41,441 Japan 23,493Spain
The average age of U.S. astronaut candidates in the past has been 34, but candidates have ranged in age from 26 to 46. Use the range rule of thumb to estimate the standard deviation of the applicants’ ages. Find the range, variance, and standard deviation unless the question asks for something
A sample of 12 drivers shows the time that they spent (in minutes) stopped in rush-hour traffic on a specific snowy day last winter. 52 56 53 61 49 51 53 58 53 60 71 58 Find the range, variance, and standard deviation unless the question asks for something different. Assume the data
The number of yards gained in NFL playoff games by rookie quarterbacks is shown. 193 66 136 140 157 163 181 226 135 199 Find the range, variance, and standard deviation unless the question asks for something different. Assume the data represent samples, and use the shortcut formula for the
The number of people killed in each state from passenger vehicle crashes for a specific year is shown.Find the range, variance, and standard deviation unless the question asks for something different. Assume the data represent samples, and use the shortcut formula for the unbiased estimator to
Find the range, variance, and standard deviation for the data in Exercise 17 of Section 2–1.
Team batting averages for major league baseball in 2005 are represented below. Find the variance and standard deviation for each league. Compare the results. NL AL 0.252–0.256 4 0.256–0.261 2 0.257–0.261 6 0.262–0.267 5 0.262–0.266 1 0.268–0.273 4 0.267–0.271 4
The costs per load (in cents) of 35 laundry detergents tested by a consumer organization are shown here. Class limits Frequency 13–19 ..........2 20–26 ..........7 27–33 ........12 34–40 ..........5 41–47 ..........6 48–54 ..........1 55–61 ..........0 62–68 ..........2 Find the
Thirty automobiles were tested for fuel efficiency (in miles per gallon). This frequency distribution was obtained. Class boundaries Frequency 7.5–12.5 ..........3 12.5–17.5 ...........5 17.5–22.5 .........15 22.5–27.5 ...........5 27.5–32.5 ...........2 Find the variance and standard
The data show the number of murders in 25 selected cities. Class limits Frequency 34–96 .........13 97–159 .........2 160–222 .......0 223–285 .......5 286–348 .......1 349–411 .......1 412–474 .......0 475–537 .......1 538–600 .......2 Find the variance and standard deviation.
In a study of reaction times to a specific stimulus, a psychologist recorded these data (in seconds). Class limits Frequency 2.1–2.7 .......12 2.8–3.4 .......13 3.5–4.1 .........7 4.2–4.8 .........5 4.9–5.5 .........2 5.6–6.2 .........1 Find the variance and standard deviation.
A random sample of 30 states shows the number of low-power FM radio stations for each state. Class limits Frequency 1–9 .........5 10–18 ..............7 19–27 ........10 28–36 ........3 37–45 ........3 46–54 ........2 Find the variance and standard deviation.
The data represent the murder rate per 100,000 individuals in a sample of selected cities in the United States.Class Frequency5–11......812–18...... 519–25.......726–32.......133–39.......140–46.......3Find the variance and standard deviation.
Eighty randomly selected batteries were tested to determine their lifetimes (in hours). The following frequency distribution was obtained. Class boundaries Frequency 62.5–73.5..........5 73.5–84.5 .........14 84.5–95.5
Find the variance and standard deviation for the two distributions in Exercises 8 and 18 in Section 2–2. Compare the variation of the data sets. Decide if one data set is more variable than the other.Find the variance and standard deviation.
This frequency distribution represents the data obtained from a sample of word processor repairers. The values are the days between service calls on 80 machines. Class boundaries Frequency 25.5–28.5 .........5 28.5–31.5 .........9 31.5–34.5 .........32 34.5–37.5 .........20 37.5–40.5
The average number of days construction workers miss per year is 11. The standard deviation is 2.3. The average number of days factory workers miss per year is 8 with a standard deviation of 1.8. Which class is more variable in terms of days missed?
The lengths (in feet) of the main span of the longest suspension bridges in the United States and the rest of the world are shown below. Which set of data is more variable? United States: 4205, 4200, 3800, 3500, 3478, 2800, 2800, 2310 World: 6570, 5538, 5328, 4888, 4626, 4544, 4518, 3970
The mean of the waiting times in an emergency room is 80.2 minutes with a standard deviation of 10.5 minutes for people who are admitted for additional treatment. The mean waiting time for patients who are discharged after receiving treatment is 120.6 minutes with a standard deviation of 18.3
The average age of the accountants at Three Rivers Corp. is 26 years, with a standard deviation of 6 years; the average salary of the accountants is $31,000, with a standard deviation of $4000. Compare the variations of age and income.
Using Chebyshev’s theorem, solve these problems for a distribution with a mean of 80 and a standard deviation of 10.a. At least what percentage of values will fall between 60 and 100? 75%b. At least what percentage of values will fall between 65 and 95?
The mean of a distribution is 20 and the standard deviation is 2. Use Chebyshev’s theorem.a. At least what percentage of the values will fall between 10 and 30? b. At least what percentage of the values will fall between 12 and 28?
In a distribution of 160 values with a mean of 72, at least 120 fall within the interval 67–77. Approximately what percentage of values should fall in the interval 62–82? Use Chebyshev’s theorem.
The average number of calories in a regularsize bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie. Use Chebyshev’s theorem.
Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, find the range in which at least 88.89% of the data will lie. Use Chebyshev’s theorem.
The average college student produces 640 pounds of solid waste each year. If the standard deviation is approximately 85 pounds, within what weight limits will at least 88.89% of all students’garbage lie?
The average sale price of new one-family houses in the United States for 2003 was $246,300. Find the range of values in which at least 75% of the sale prices will lie if the standard deviation is $48,500.
The average of the number of trials it took a sample of mice to learn to traverse a maze was 12. The standard deviation was 3. Using Chebyshev’s theorem, find the minimum percentage of data values that will fall in the range of 4–20 trials.
The average farm in the United States in 2004 contained 443 acres. The standard deviation is 42 acres. Use Chebyshev’s theorem to find the minimum percentage of data values that will fall in the range of 338–548 acres.
The average U.S. yearly per capita consumption of citrus fruit is 26.8 pounds. Suppose that the distribution of fruit amounts consumed is bell-shaped with a standard deviation equal to 4.2 pounds. What percentage of Americans would you expect to consume more than 31 pounds of citrus fruit per year?
The average full-time faculty member in a post-secondary degree-granting institution works an average of 53 hours per week.a. If we assume the standard deviation is 2.8 hours, what percentage of faculty members work more than 58.6 hours a week? No more than 12.5%b. If we assume a bell-shaped
For this data set, find the mean and standard deviation of the variable. The data represent the serum cholesterol levels of 30 individuals. Count the number of data values that fall within 2 standard deviations of the mean. Compare this with the number obtained from Chebyshev€™s theorem.
For this data set, find the mean and standard deviation of the variable. The data represent the ages of 30 customers who ordered a product advertised on television. Count the number of data values that fall within 2 standard deviations of the mean. Compare this with the number obtained from
Using Chebyshev€™s theorem, complete the table to find the minimum percentage of data values that fall within k standard deviations of the mean.
Use this data set: 10, 20, 30, 40, 50a. Find the standard deviation. b. Add 5 to each value, and then find the standard deviation. c. Subtract 5 from each value and find the standard deviation. d. Multiply each value by 5 and find the standard deviation. e. Divide each value by 5 and find the
The mean deviation is found by using this formula:whereX = value= meann = number of values| | = absolute valueFind the mean deviation for these data.5, 9, 10, 11, 11, 12, 15, 18, 20, 22
A measure to determine the skewness of a distribution is called the Pearson coefficient of skewness (PC). The formula isThe values of the coefficient usually range from €“ 3 to + 3. When the distribution is symmetric, the coefficient is zero; when the distribution is positively skewed, it is
All values of a data set must be within s√ n – 1of the mean. If a person collected 25 data values that had a mean of 50 and a standard deviation of 3 and you saw that one data value was 67, what would you conclude?
The three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples.a. 5, 7, 9, 11, 13, 15, 17b. 5, 6, 7, 11, 15, 16, 17c. 5, 5, 5, 11, 17, 17, 17
The number of incidents in which police were needed for a sample of 10 schools in Allegheny County is 7, 37, 3, 8, 48, 11, 6, 0, 10, 3. Are the data consistent or do they vary? Explain your answer. Find the range, variance, and standard deviation unless the question asks for something
The increases (in cents) in cigarette taxes for 17 states in a 6-month period are60, 20, 40, 40, 45, 12, 34, 51, 30, 70, 42, 31, 69, 32, 8, 18, 50Use the range rule of thumb to estimate the standard deviation. Compare the estimate to the actual standard deviation. Find the range, variance, and
The normal daily high temperatures (in degrees Fahrenheit) in January for 10 selected cities are as follows.50, 37, 29, 54, 30, 61, 47, 38, 34, 61The normal monthly precipitation (in inches) for these same 10 cities is listed here.4.8, 2.6, 1.5, 1.8, 1.8, 3.3, 5.1, 1.1, 1.8, 2.5Which set is more
The average age of Senators in the 108th Congress was 59.5 years. If the standard deviation was 11.5 years, find the z scores corresponding to the oldest and youngest Senators: Robert C. Byrd (D, WV), 86, and John Sununu (R, NH), 40.
The average score on a state CDL license exam is 76 with a standard deviation of 5. Find the corresponding z score for each raw score.a. 79 b. 70 c. 88d. 65e. 77
The average teacher’s salary in a particular state is $54,166. If the standard deviation is$10,200, find the salaries corresponding to the following z scores.a. 2 b. – 1 c. 0 d. 2.5 e. –1.6
Which has a better relative position: a score of 75 on a statistics test with a mean of 60 and a standard deviation of 10 or a score of 36 on an accounting test with a mean of 30 and a variance of 16?
A student graduated from a 4-year college with an outstanding loan of $9650 where the average debt is $8455 with a standard deviation of $1865. Another student graduated from a university with an outstanding loan of $12,360 where the average of the outstanding loans was $10,326 with a standard
Which score indicates the highest relative position?a. A score of 3.2 on a test with = 4.6 and s = 1.5 b. A score of 630 on a test with = 800 and s = 200 c. A score of 43 on a test with = 50 and s = 5
Room and board costs for selected schools are summarized in this distribution. Find the approximate cost of room and board corresponding to each of the following percentiles.Costs (in dollars) Frequency3000.5–4000.5 .....54000.5–5000.5 .....65000.5–6000.5 .....186000.5–7000.5
Using the data in Exercise 16, find the approximate percentile rank of each of the following costs.a. 5500 b. 7200 c. 6500 d. 8300
The data shown represent the scores on a national achievement test for a group of 10th-grade students. Find the approximate percentile ranks of these scores by constructing a percentile graph.a. 220 b. 245 c. 276 d. 280 e. 300 Score Frequency196.5–217.5........5217.5–238.5
For the data in Exercise 18, find the approximate scores that correspond to these percentiles.a. 15th b. 29th c. 43rd d. 65th e. 80th
The airborne speeds in miles per hour of 21 planes are shown. Find the approximate values that correspond to the given percentiles by constructing a percentile graph.Class Frequency366–386.....4387–407 .......2408–428 .......3429–449 .......2450–470 .......1471–491 .......2492–512
Using the data in Exercise 20, find the approximate percentile ranks of the following miles per hour (mph).a. 380 mph 13th b. 425 mph 40th c. 455 mph 54thd. 505 mph 76the. 525 mph 92nd
The average weekly earnings in dollars for various industries are listed below. Find the percentile rank of each value. 804 736 659 489 777 623 597 524 228
Find the percentile rank for each test score in the data set. 12, 28, 35, 42, 47, 49, 50
In Exercise 24, what value corresponds to the 60th percentile?
Find the percentile rank for each value in the data set. The data represent the values in billions of dollars of the damage of 10 hurricanes.
What value in Exercise 26 corresponds to the 40th percentile?
Test Scores Find the percentile rank for each test score in the data set.5, 12, 15, 16, 20, 21
What test score in Exercise 28 corresponds to the 33rd percentile?
Using the procedure shown in Example 3–37, check each data set for outliers.a. 16, 18, 22, 19, 3, 21, 17, 20 b. 24, 32, 54, 31, 16, 18, 19, 14, 17, 20 c. 321, 343, 350, 327, 200 d. 88, 72, 97, 84, 86, 85, 100 e. 145, 119, 122, 118, 125, 116 145f. 14, 16, 27, 18, 13, 19, 36, 15, 20

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