Chapter 2

A set of data consists of 45 observations between \(\$ 0\) and \(\$ 29 .\) What size would you recommend for the class interval?

A set of data consists of 230 observations between \(\$ 235\) and \(\$ 567 .\) What class interval would you recommend?

Wachesaw Manufacturing, Inc. produced the following number of units the last 16 days. $$ \begin{array}{|llllllll|} \hline 27 & 27 & 27 & 28 & 27 & 25 & 25 & 28 \\ 26 & 28 & 26 & 28 & 31 & 30 & 26 & 26 \\ \hline \end{array} $$ The information is to be organized into a frequency distribution. a. How many classes would you recommend? b. What class interval would you suggest? c. What lower limit would you recommend for the first class? d. Organize the information into a frequency distribution and determine the relative frequency distribution. e. Comment on the shape of the distribution.

Ecommerce.com, a large Internet retailer, is studying the lead time (elapsed time between when an order is placed and when it is filled) for a sample of recent orders. The lead times are reported in days. $$ \begin{array}{|cc|} \hline \text { Lead Time (days) } & \text { Frequency } \\ \hline 0 \text { up to } 5 & 6 \\ 5 \text { up to } 10 & 7 \\ 10 \text { up to } 15 & 12 \\ 15 \text { up to } 20 & 8 \\ 20 \text { up to } 25 & \frac{7}{40} \\ \text { Total } & 40 \\ \hline \end{array} $$ a. How many orders were studied? b. What is the midpoint of the first class? c. What are the coordinates of the first class for a frequency polygon? d. Draw a histogram. e. Draw a frequency polygon. f. Interpret the lead times using the two charts.

The frequency distribution representing the number of frequent flier miles accumulated by employees at Brumley Statistical Consulting Company is repeated from Exercise \(11 .\) $$ \begin{array}{|cc|} \hline \begin{array}{c} \text { Frequent Flier Miles } \\ (000) \end{array} & \text { Frequency } \\ \hline 0 \text { up to } 3 & 5 \\ 3 \text { up to } 6 & 12 \\ 6 \text { up to } 9 & 23 \\ 9 \text { up to } 12 & 8 \\ 12 \text { up to } 15 & 2 \\ \text { Total } & \frac{2}{50} \\ \hline \end{array} $$a. How many employees accumulated less than 3,000 miles? b. Convert the frequency distribution to a cumulative frequency distribution. c. Portray the cumulative distribution in the form of a cumulative frequency polygon. d. Based on the cumulative frequency polygon, about 75 percent of the employees accumulated how many miles or less?

A small business consultant is investigating the performance of several companies. The sales in 2004 (in thousands of dollars) for the selected companies were: $$ \begin{array}{|lr|} \hline \text { Corporation } & \begin{array}{c} \text { Fourth-Quarter Sales } \\ \text { (\$ thousands) } \end{array} \\ \hline \text { Hoden Building Products } & \$ 1,645.2 \\ \text { J \& R Printing, Inc. } & 4,757.0 \\ \text { Long Bay Concrete Construction } & 8,913.0 \\ \text { Mancell Electric and Plumbing } & 627.1 \\ \text { Maxwell Heating and Air Conditioning } & 24,612.0 \\ \text { Mizelle Roofing \& Sheet Metals } & 191.9 \\ \hline \end{array} $$ The consultant wants to include a chart in his report comparing the sales of the six companies. Use a bar chart to compare the fourth quarter sales of these corporations and write a brief report summarizing the bar chart.

The Blair Corporation, located in Warren, Pennsylvania, sells fashion apparel for men and women plus a broad range of home products (http://www.blair.com). It services its customers by mail. Listed below are the net sales for Blair from 1998 through \(2003 .\) Draw a line chart depicting the net sales over the time period and write a brief report. $$ \begin{array}{|lc|} \hline \text { Year } & \begin{array}{c} \text { Net Sales } \\ \text { (\$ millions) } \end{array} \\ \hline 1998 & 506.8 \\ 1999 & 522.2 \\ 2000 & 574.6 \\ 2001 & 580.7 \\ 2002 & 568.5 \\ 2003 & 581.9 \\ \end{array} $$

A headline in a Toledo, Ohio, newspaper reported that crime was on the decline. Listed below are the number of homicides from 1986 to \(2003 .\) Draw a line chart to summarize the data and write a brief summary of the homicide rates for the last 18 years. $$ \begin{array}{|ccccc|} \hline \text { Year } & \text { Homicides } & & \text { Year } & \text { Homicides } \\ \hline 1986 & 21 & & 1995 & 35 \\ 1987 & 34 & & 1996 & 30 \\ 1988 & 26 & & 1997 & 28 \\ 1989 & 42 & & 1998 & 25 \\ 1990 & 37 & & 1999 & 21 \\ 1991 & 37 & & 2000 & 19 \\ 1992 & 44 & & 2001 & 23 \\ 1993 & 45 & & 2002 & 27 \\ 1994 & 40 & & 2003 & 23 \\ \hline \end{array} $$

A report prepared for the governor of a western state indicated that 56 percent of the state's tax revenue went to education, 23 percent to the general fund, 10 percent to the counties, 9 percent to senior programs, and the remainder to other social programs. Develop a pie chart to show the breakdown of the budqet.

The following table shows the population, in millions, of the United States in 5 -year intervals from 1950 to \(2000 .\) Develop a line chart depicting the population growth and write a brief report summarizing your findings. $$ \begin{array}{|ccccc|} \hline \text { Year } & \begin{array}{c} \text { Population } \\ \text { (millions) } \end{array} & \text { Year } & \begin{array}{c} \text { Population } \\ \text { (millions) } \end{array} \\ \hline 1950 & 152.3 & 1980 & 227.7 \\ 1955 & 165.9 & 1985 & 238.5 \\ 1960 & 180.7 & 1990 & 249.9 \\ 1965 & 194.3 & 1995 & 263.0 \\ 1970 & 205.1 & 2000 & 281.4 \\ 1975 & 216.0 & & \\ \hline \end{array} $$

Shown below are the military and civilian personnel expenditures for the eight largest military locations in the United States. Develop a bar chart and summarize the results in a brief report. $$ \begin{array}{|lclc|} \hline \text { Location } & \begin{array}{c} \text { Amount Spent } \\ \text { (millions) } \end{array} & \text { Location } & \begin{array}{c} \text { Amount Spent } \\ \text { (millions) } \end{array} \\ \hline \text { St. Louis, M0 } & \$ 6,087 & \text { Norfolk, VA } & \$ 3,228 \\\ \text { San Diego, CA } & 4,747 & \text { Marietta, GA } & 2,828 \\ \text { Pico Rivera, CA } & 3,272 & \text { Fort Worth, TX } & 2,492 \\ \text { Arlington, VA } & 3,284 & \text { Washington, DC } & 2,347 \\ \hline \end{array} $$

A dataset consists of 83 observations. How many classes would you recommend for a frequency distribution?

A dataset consists of 145 observations that range from 56 to \(490 .\) What size class interval would you recommend?

The following is the number of minutes to commute from home to work for a sample of aerospace workers in Houston, Texas. $$ \begin{array}{|lllllllllllll|} \hline 28 & 25 & 48 & 37 & 41 & 19 & 32 & 26 & 16 & 23 & 23 & 29 & 36 \\ 31 & 26 & 21 & 32 & 25 & 31 & 43 & 35 & 42 & 38 & 33 & 28 & \\ \hline \end{array} $$ a. How many classes would you recommend? b. What class interval would you suggest? c. What would you recommend as the lower limit of the first class? d. Organize the data into a frequency distribution. e. Comment on the shape of the frequency distribution.

A chain of sport shops catering to beginning skiers, headquartered in Aspen, Colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. Based on these figures, they want to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. A sample of their cash register receipts revealed these initial purchases: $$ \begin{array}{rrrrrrrrr} \hline \$ 140 & \$ 82 & \$ 265 & \$ 168 & \$ 90 & \$ 114 & \$ 172 & \$ 230 & \$ 142 \\ 86 & 125 & 235 & 212 & 171 & 149 & 156 & 162 & 118 \\ 139 & 149 & 132 & 105 & 162 & 126 & 216 & 195 & 127 \\ 161 & 135 & 172 & 220 & 229 & 129 & 87 & 128 & 126 \\ 175 & 127 & 149 & 126 & 121 & 118 & 172 & 126 & \\ \hline \end{array} $$ a. Arrive at a suggested class interval. Use five classes, and let the lower limit of the first class be \(\$ 80\). b. What would be a better class interval? c. Organize the data into a frequency distribution using a lower limit of \(\$ 80\). d. Interpret your findings.

The numbers of shareholders for a selected group of large companies (in thousands) are: $$ \begin{array}{|lclc|} \hline & \begin{array}{c} \text { Number of } \\ \text { Shareholders } \\ \text { (thousands) } \end{array} & \text { Company } & \begin{array}{c} \text { Number of } \\ \text { Shareholders } \\ \text { (thousands) } \end{array} \\ \text { Company } & 144 & \text { Standard Oil (Indiana) } & 173 \\ \text { Southwest Airlines } & 177 & \text { Home Depot } & 195 \\ \text { General Public Utilities } & 266 & \text { Detroit Edison } & 220 \\ \text { Occidental Petroleum } & 133 & \text { Eastman Kodak } & 251 \\ \text { Middle South Utilities } & 209 & \text { Dow Chemical } & 137 \\ \text { DaimlerChrysler } & 264 & \text { Pennsylvania Power } & 150 \\ \text { Standard Oil of California } & 160 & \text { American Electric Power } & 262 \\ \text { Bethlehem Steel } & 143 & \text { Ohio Edison } & 158 \\ \text { Long Island Lighting } & 246 & \text { Transamerica Corporation } & 162 \\ \text { RCA } & 151 & \text { Columbia Gas System } & 165 \\ \text { Greyhound Corporation } & 239 & \text { International Telephone \& } & \\\ \text { Pacific Gas \& Electric } & 204 & \text { Telegraph } & 223 \\ \text { Niagara Mohawk Power } & 204 & \text { Union Electric } & 158 \\ \text { E.l: du Pont de Nemours } & 195 & \text { Virginia Electric and Power } & 162 \\ \text { Morris Knudsen Corporation } & 176 & \text { Public Service Electric \& Gas } & 225 \\ \text { Union Carbide } & 175 & \text { Consumers Power } & 161 \\ \text { BankAmerica } & 200 & & \\ \text { Northeast Utilities } & & & & \\ \hline \end{array} $$ The numbers of shareholders are to be organized into a frequency distribution and several graphs drawn to portray the distribution. a. Using seven classes and a lower limit of \(130,\) construct a frequency distribution. b. Portray the distribution as a frequency polygon. c. Portray the distribution in a cumulative frequency polygon. d. According to the polygon, three out of four \((75\) percent) of the companies have how many shareholders or less? e. Write a brief analysis of the number of shareholders based on the frequency distribution and graphs.

The Midland National Bank selected a sample of 40 student checking accounts. Below are their end-of-the-month balances. $$ \begin{array}{rrrrrrrrrr} \hline \$ 404 & \$ 74 & \$ 234 & \$ 149 & \$ 279 & \$ 215 & \$ 123 & \$ 55 & \$ 43 & \$ 321 \\ 87 & 234 & 68 & 489 & 57 & 185 & 141 & 758 & 72 & 863 \\ 703 & 125 & 350 & 440 & 37 & 252 & 27 & 521 & 302 & 127 \\ 968 & 712 & 503 & 489 & 327 & 608 & 358 & 425 & 303 & 203 \\ \hline \end{array} $$ a. Tally the data into a frequency distribution using \(\$ 100\) as a class interval and \(\$ 0\) as the starting point. b. Draw a cumulative frequency polygon. c. The bank considers any student with an ending balance of \(\$ 400\) or more a "preferred customer." Estimate the percentage of preferred customers. d. The bank is also considering a service charge to the lowest 10 percent of the ending bal- ances. What would you recommend as the cutoff point between those who have to pay a service charge and those who do not?

Residents of the state of South Carolina earned a total of \(\$ 70.6\) billion in 2003 in adjusted gross income. Seventy-three percent of the total was in wages and salaries; 11 percent in dividends, interest, and capital gains; 8 percent in IRAs and taxable pensions; 3 percent in business income pensions; 2 percent in social security, and the remaining 3 percent was from other sources. Develop a pie chart depicting the breakdown of adjusted gross income. Write a paragraph summarizing the information.

A recent study of home technologies reported the number of hours of personal computer usage per week for a sample of 60 persons. Excluded from the study were people who worked out of their home and used the computer as a part of their work. $$ \begin{array}{|rrrrrrrrrr|} \hline 9.3 & 5.3 & 6.3 & 8.8 & 6.5 & 0.6 & 5.2 & 6.6 & 9.3 & 4.3 \\ 6.3 & 2.1 & 2.7 & 0.4 & 3.7 & 3.3 & 1.1 & 2.7 & 6.7 & 6.5 \\ 4.3 & 9.7 & 7.7 & 5.2 & 1.7 & 8.5 & 4.2 & 5.5 & 5.1 & 5.6 \\ 5.4 & 4.8 & 2.1 & 10.1 & 1.3 & 5.6 & 2.4 & 2.4 & 4.7 & 1.7 \\ 2.0 & 6.7 & 1.1 & 6.7 & 2.2 & 2.6 & 9.8 & 6.4 & 4.9 & 5.2 \\ 4.5 & 9.3 & 7.9 & 4.6 & 4.3 & 4.5 & 9.2 & 8.5 & 6.0 & 8.1 \\ \hline \end{array} $$ a. Organize the data into a frequency distribution. How many classes would you suggest? What value would you suggest for a class interval? b. Draw a histogram. Interpret your result.

In May 2004,18.5 percent of the Prime Time TV viewing audience watched shows on \(\mathrm{ABC}\), 25.9 percent on CBS, 18.5 percent on Fox, 18.5 percent on \(\mathrm{NBC}, 7.4\) percent on Warner Brothers, and 7.4 percent on UPN. You can find the latest information on TV viewing from the following website: http://tv.zap2it.com/news/ratings/. Develop a pie chart or a bar chart to depict this information. Write a paragraph summarizing the information.

The American Heart Association reported the following percentage breakdown of expenses. Draw a pie chart depicting the information. Interpret. $$ \begin{array}{|lr|} \hline \text { Category } & \text { Percent } \\ \hline \text { Research } & 32.3 \\ \text { Public Health Education } & 23.5 \\ \text { Community Service } & 12.6 \\ \text { Fund Raising } & 12.1 \\ \text { Professional and Educational Training } & 10.9 \\ \text { Management and General } & 8.6 \\ \hline \end{array} $$

Annual revenues, by type of tax, for the state of Georgia are as follows. Develop an appropriate chart or graph and write a brief report summarizing the information. $$ \begin{array}{|lr|} \hline \text { Type of Tax } & \text { Amount (000) } \\ \hline \text { Sales } & \$ 2,812,473 \\ \text { Income (Indlividual) } & 2,732,045 \\ \text { License } & 185,198 \\ \text { Corporate } & 525,015 \\ \text { Property } & 22,647 \\ \text { Death and Gift } & 37,326 \\ \text { Total } & \$ 6,314,704 \\ \hline \end{array} $$

Annual imports from selected Canadian trading partners are listed below for the year \(2003 .\) Develop an appropriate chart or graph and write a brief report summarizing the information. $$ \begin{array}{|lr|} \hline \text { Partner } & \begin{array}{c} \text { Annual Imports } \\ \text { (million) } \end{array} \\ \hline \text { Japan } & \$ 9,550 \\ \text { United Kingdom } & 4,556 \\ \text { South Korea } & 2,441 \\ \text { China } & 1,182 \\ \text { Australia } & 618 \\ \hline \end{array} $$

Farming has changed from the early 1900 s. In the early 20 th century, machinery gradually replaced animal power. For example, in 1910 U.S. farms used 24.2 million horses and mules and only about 1,000 tractors. By 1960,4.6 million tractors were used and only 3.2 million horses and mules. In 1920 there were over 6 million farms in the United States. Today there are less than 2 million. Listed below is the number of farms, in thousands, for each of the 50 states. Write a paragraph summarizing your findings.

One of the most popular candies in the United States is M\&M's, which are produced by the Mars Company. In the beginning M\&M's were all brown; more recently they were produced in red, green, blue, orange, brown, and yellow. You can read about the history of the product, find ideas for baking, purchase the candies in the colors of your school or favorite team, and learn the percent of each color in the standard bags at http://global.mms.com/us/about/products/milkchocolate.jsp. Recently the purchase of a 14-ounce bag of M\&M's Plain had 444 candies with the following breakdown by color: 130 brown, 98 yellow, 96 red, 35 orange, 52 blue, and 33 green. Develop a chart depicting this information and write a paragraph summarizing the results.

A pie chart shows the market shares of cola products. The "slice" for Pepsi- Cola has a central angle of 90 degrees. What is their market share?