Chapter 3

Compute the mean of the following population values: 6,3,5,7,6

Compute the mean of the following population values: 7,5,7,3,7,4

Compute the mean of the following sample values: 16.25,12.91,14.58

Compute the mean hourly wage paid to carpenters who earned the following hourly wages: \(\$ 15.40, \$ 20.10\), \(\$ 18.75, \$ 22.76, \$ 30.67, \$ 18.00 .\)

(A) compute the arithmetic mean and (B) indicate whether it is a statistic or a parameter. There are 10 salespeople employed by Midtown Ford. The number of new cars sold last month by the respective salespeople were: \(15,23,4,19,18,10,10,8,\) 28,19

(A) compute the arithmetic mean and (B) indicate whether it is a statistic or a parameter. The accounting department at a mail-order company counted the following numbers of incoming calls per day to the company's toll-free number during the first 7 days in May 2007: 14,24,19,31,36,26,17

AAA Heating and Air Conditioning completed 30 jobs last month with a mean revenue of \(\$ 5,430\) per job. The president wants to know the total revenue for the month. Based on the limited information, can you compute the total revenue? What is it?

In June an investor purchased 300 shares of Oracle (an information technology company) stock at \(\$ 20\) per share. In August she purchased an additional 400 shares at \(\$ 25\) per share. In November she purchased an additional 400 shares, but the stock declined to \(\$ 23\) per share. What is the weighted mean price per share?

The Bookstall, Inc., is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are \(\$ 1.00\) each, and hardcover books are \(\$ 3.50 .\) Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?

The Bookstall, Inc., is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are \(\$ 1.00\) each, and hardcover books are \(\$ 3.50 .\) Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?

Andrews and Associates specialize in corporate law. They charge \(\$ 100\) an hour for researching a case, \(\$ 75\) an hour for consultations, and \(\$ 200\) an hour for writing a brief. Last week one of the associates spent 10 hours consulting with her client, 10 hours researching the case, and 20 hours writing the brief. What was the weighted mean hourly charge for her legal services?

What would you report as the modal value for a set of observations if there were a totalof: a. 10 observations and no two values were the same? b. 6 observations and they were all the same? c. 6 observations and the values were \(1,2,3,3,4,\) and \(4 ?\) For Exercises \(18-20,\) determine the (a) mean, (b) median, and (c) mode.

Compute the geometric mean of the following percent increases: \(8,12,14,26,\) and \(5 .\)

Compute the geometric mean of the following percent increases: \(2,8,6,4,10,6,8,\) and 4

In 1996 a total of 14,968,000 taxpayers in the United States filed their individual tax returns electronically. By the year 2006 the number increased to 73,300,000 . What is the geometric mean annual increase for the period?

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 1994 was 148.2 , by 2006 it increased to 200.6 . What was the geometric mean annual increase for the period?

In 1976 the nationwide average price of a gallon of unleaded gasoline at a self-serve pump was \(\$ 0.605 .\) By 2007 the average price had increased to \(\$ 2.57 .\) What was the qeometric mean annual increase for the period?

In 2001 there were 42.0 million pager subscribers. By 2006 the number of subscribers increased to 70.0 million. What is the geometric mean annual increase for the period?

There were five customer service representatives on duty at the Electronic Super Store during last weekend's sale. The numbers of HDTVs these representatives sold are: \(5,8,4,10,\) and 3

Consider these five values a population: \(8,3,7,3,\) and 4 a. Determine the mean of the population. b. Determine the variance.

Consider these six values a population: 13,3,8,10,8 , and 6 . a. Determine the mean of the population. b. Determine the variance.

The annual report of Dennis Industries cited these primary earnings per common share for the past 5 years: \(\$ 2.68, \$ 1.03, \$ 2.26, \$ 4.30,\) and \(\$ 3.58 .\) If we assume these are population values, what is: a. The arithmetic mean primary earnings per share of common stock? b. The variance?

Plywood, Inc., reported these returns on stockholder equity for the past 5 years: \(4.3,4.9,7.2,6.7,\) and \(11.6 .\) Consider these as population values. a. Compute the range, the arithmetic mean, the variance, and the standard deviation. b Comnare the return on stockholder ea

46\. The annual incomes of the five vice presidents of TMV Industries are: \(\$ 125,000 ; \quad \$ 128,000 ; \quad \$ 122,000 ;\) \(\$ 133,000 ;\) and \(\$ 140,000 .\) Consider this a population. a. What is the range? b. What is the arithmetic mean income? c. What is the population variance? The standard deviation? d. The annual incomes of officers of another firm similar to TMV Industries were also studied. The mean was \(\$ 129,000\) and the standard deviation \(\$ 8,612 .\) Compare the means and dispersions in the two firms.

For Exercises \(47-52,\) do the following: a. Compute the sample variance. b. Determine the sample standard deviation. Consider these values a sample: \(7,2,6,2,\) and \(3 .\)

Do the following: a. Compute the sample variance. b. Determine the sample standard deviation. The following five values are a sample: 11,6,10,6 , and 7 .

Do the following: a. Compute the sample variance. b. Determine the sample standard deviation. Dave's Automatic Door, referred to in Exercise 37 . installs automatic garage door openers. Based on a sample, following are the times, in minutes, required to install 10 door openers: \(28,32,24,46,44,40,54,38,\) \(32,\) and 42

Do the following: a. Compute the sample variance. b. Determine the sample standard deviation. The sample of eight companies in the aerospace industry, referred to in Exercise \(36,\) was surveyed as to their return on investment last year. The results are: \(10.6,12.6,14.8,18.2,12.0,14.8,12.2,\) and \(15.6 .\)

According to Chebyshev's theorem, at least what percent of any set of observations will be within 1.8 standard deviations of the mean?

The mean income of a group of sample observations is \(\$ 500\); the standard deviation is \(\$ 40\). According to Chebyshev's theorem, at least what percent of the incomes will lie between \(\$ 400\) and \(\$ 600 ?\)

The distribution of the weights of a sample of 1,400 cargo containers is symmetric and bell-shaped. According to the Empirical Rule, what percent of the weights will lie: a. Between \(x-2\) and \(\bar{x}+2 s ?\) b. Between \(\bar{x}\) and \(\bar{x}+2\) s? Below \(\bar{x}-2 s ?\)

The following graph portrays the distribution of the number of Biggie-sized soft drinks sold at a nearby Wendy's for the last 141 days. The mean number of drinks sold per day is 91.9 and the standard deviation is 4.67 If we use the Empirical Rule, sales will be between what two values on 68 percent of the days? Sales will be between what two values on 95 percent of the days?

The accounting firm of Crawford and Associates has five senior partners. Yesterday the senior partners saw six, four, three, seven, and five clients, respectively. a. Compute the mean number and median number of clients seen by a partner. b. Is the mean a sample mean or a population mean? Why? c. Verify that \(\Sigma(X-\mu)=0\).

Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23,19,26,17,21,24,22 a. Compute the mean number and median number of apples in a bag. b. Verify that \(\Sigma(x-\bar{x})=0\)

The Split-A-Rail Fence Company sells three types of fence to homeowners in suburban Seattle, Washington. Grade A costs \(\$ 5.00\) per running foot to install, Grade \(B\) costs \(\$ 6.50\) per running foot, and Grade \(C,\) the premium quality, costs \(\$ 8.00\) per running foot. Yesterday, Split-ARail installed 270 feet of Grade \(\mathrm{A}, 300\) feet of Grade \(\mathrm{B}\), and 100 feet of Grade \(C\). What was the mean cost per foot of fence installed?

Rolland Poust is a sophomore in the College of Business at Scandia Tech. Last semester he took courses in statistics and accounting, 3 hours each, and earned an \(\mathrm{A}\) in both. He earned a \(\mathrm{B}\) in a five-hour history course and a \(\mathrm{B}\) in a two-hour history of jazz course. In addition, he took a one-hour course dealing with the rules of basketball so he could get his license to officiate high school basketball games. He got an A in this course. What was his GPA for the semester? Assume that he receives 4 points for an \(\mathrm{A}, 3\) for \(\mathrm{a} \mathrm{B},\) and so on. What measure of location did you just calculate?

The metropolitan area of Los Angeles-Long Beach, California, is the area expected to show the largest increase in the number of jobs between 1989 and 2010 . The number of jobs is expected to increase from 5,164,900 to 6,286,800 . What is the geometric mean expected vearly rate of increase?

A recent article suggested that, it you earn \(\$ 25,000\) a year today and the inflation rate continues at 3 percent per year, you'll need to make \(\$ 33,598\) in 10 years to have the same buying power. You would need to make \(\$ 44,771\) if the inflation rate jumped to 6 percent. Confirm that these statements are accurate by finding the geometric mean rate of increase.

The ages of a sample of Canadian tourists flying from Toronto to Hong Kong were: \(32,21,60,47,54,17,72,\) \(55,33,\) and 41 a. Compute the range. b. Compute the mean deviation. c. Compute the standard deviation.

The weights (in pounds) of a sample of five boxes being sent by UPS are: \(12,6,7,3,\) and \(10 .\) a. Compute the range. b. Compute the mean deviation. c. Compute the standard deviation.

A southern state has seven state universities in its system. The numbers of volumes (in thousands) held in its libraries are \(83,510,33,256,401,47,\) and \(23 .\) a. Is this a sample or a population? b. Compute the standard deviation.

The State of Indiana and the Kelley School of Business of Indiana University offer links to many data sources. Go to www.stats.indiana.edu, then, under the heading Social and Economic indicators select Birth/Marriage/Death, under state comparisons, select Annual Vital Statistics Data, for Geography Type choose U.S. and 50 States, for Specific Geography select all states, and finally select Get Data. The information can be output in Excel format. Suppose you are interested in the typical number of births per state. Compute the mean, median, and the standard deviation of the number of births per state and the number of births per 1000 population by state for the latest year available. You should be able to download this information into a software package to perform the calculations. Which of the measures of location is the most representative? Which data set would you recommend using: number of births per state or the number of births per 1000 population? Why? Suppose you are interested in birth rates for the 50 states and Washington, D.C. Compute the mean, median, and standard deviation. Write a brief report summarizing the data.

There are many financial websites that provide information on stocks by industry. For example, go to http://finance.yahoo.com and select Stock Research under Analyst Research select Sector/Industry Analysis. There are many choices available here such as Healthcare. Another list of choices is now available; select one such as Drug Manufacturers-Major. A list of companies in that industry will appear. Select one of the variables available, such as the price to earnings ratio, listed as \(\mathbf{P} / \mathbf{E} .\) This variable is the ratio of the selling price of a share of the company's common stock to the earnings per share of common stock. Download this information into Excel and find the mean, median, and standard deviation. Go back to Sector/Industry Analysis and choose another sector and industry. You might want to select Utilities and then Gas Utilities. A list of companies will appear. Select the same variable as before. Download the information to Excel and find the mean, median, and standard deviation for this industry. Compare the information on the two sectors. Write a brief report summarizing your findings. Are the means different? Is there more variability in one industry than another?