Descriptive and inferential statistics | Management homework help

Word count is not measured; however, ensure there is enough discussion to have a substantial response. 

Due by Thursday (55 points)

Initial Discussion. Respond to each of the following 11 questions: 

Read and understand the selected learning objectives in the Lind et al. (2021) textbook. 

Chapter 1: LO1-3 Descriptive Statistics; LO1-3 Inferential Statistics; LO1-5 Levels of Measurement

Chapter 2: LO2-1 Frequency Table; LO2-2 Chart Types

Chapter 1

1A. Describe the purpose of Descriptive Statistics

1B. Describe the purpose of Inferential Statistics

1C. Describe in your own words the difference between descriptive and inferential statistics. 

Share two business scenarios each. You may draw on business scenarios from your work or personal experience, or from the Lind textbook.

1D1. Descriptive statistics would be more effective

1D2. Inferential statistics would be more effective. 

E. List the characteristics in each type that make it more suitable for one approach over the other.

Levels of Measurement – Identify each as Nominal, Ordinal, Interval, or Ratio

1F1. Individual social security numbers.

1F2. Distance students travel to the grocery store.

1F3. The difference in mileage between Houston and Dallas.

1F4. A student’s academic class – freshman, sophomore, junior, or senior.

Chapter 2

2A. Give an example of how a Frequency Table could be used at work.

2B. List the charts used with Qualitative Data.

Types of StatisticsLO1-3Differentiate between descriptive and inferential statistics.When we use statistics to generate information for decision making from data, we use either descriptive statistics or inferential statistics. Their application depends on the questions asked and the type of data available.Descriptive StatisticsMasses of unorganized data—such as the census of population, the weekly earnings of thousands of computer programmers, and the individual responses of 2,000 registered voters regarding their choice for president of the United States—are of little value as is. However, descriptive statistics can be used to organize data into a meaningful form. We define descriptive statistics as:DESCRIPTIVE STATISTICS Methods of organizing, summarizing, and presenting data in an informative way.The following are examples that apply descriptive statistics to summarize a large amount of data and provide information that is easy to understand.There are a total of 46,837 miles of interstate highways in the United States. The interstate system represents only 1% of the nation’s total roads but carries more than 20% of the traffic. The longest is I-90, which stretches from Boston to Seattle, a distance of 3,099 miles. The shortest is I-878 in New York City, which is 0.70 mile in length. Alaska does not have any interstate highways, Texas has the most interstate miles at 3,232, and New York has the most interstate routes with 28.Americans spent an average of $143.56 on Valentine’s Day–related gifts in 2018. About 15 percent of Americans purchased gifts cards for Valentine’s Day. In addition, they spent an average of $5.50 on gifts for their pets. (www.cnn.com/2018/02/14/us/valentines-by-the-numbers-trnd/index.html)Statistical methods and techniques to generate descriptive statistics are presented in Chapters 2 and 4. These include organizing and summarizing data with frequency distributions and presenting frequency distributions with charts and graphs. In addition, statistical measures to summarize the characteristics of a distribution are discussed in Chapter 3.page 5 Inferential StatisticsSometimes we must make decisions based on a limited set of data. For example, we would like to know the operating characteristics, such as fuel efficiency measured by miles per gallon, of sport utility vehicles (SUVs) currently in use. If we spent a lot of time, money, and effort, all the owners of SUVs could be surveyed. In this case, our goal would be to survey the population of SUV owners.POPULATION The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.However, based on inferential statistics, we can survey a limited number of SUV owners and collect a sample from the population.SAMPLE A portion, or part, of the population of interest.Samples often are used to obtain reliable estimates of population parameters. (Sampling is discussed in Chapter 8.) In the process, we make trade-offs between the time, money, and effort to collect the data and the error of estimating a population parameter. The process of sampling SUVs is illustrated in the following graphic. In this example, we would like to know the mean or average SUV fuel efficiency. To estimate the mean of the population, six SUVs are sampled and the mean of their MPG is calculated. STATISTICS IN ACTIONWhere did statistics get its start? In 1662 John Graunt published an article called “Natural and Political Observations Made upon Bills of Mortality.” The author’s “observations” were the result of a study and analysis of a weekly church publication called “Bill of Mortality,” which listed births, christenings, and deaths and their causes. Graunt realized that the Bills of Mortality represented only a fraction of all births and deaths in London. However, he used the data to reach broad conclusions or inferences about the impact of disease, such as the plague, on the general population. His logic is an example of statistical inference. His analysis and interpretation of the data are thought to mark the start of statistics.So, the sample of six SUVs represents evidence from the population that we use to reach an inference or conclusion about the average MPG for all SUVs. The process of sampling from a population with the objective of estimating properties of a population is called inferential statistics.INFERENTIAL STATISTICS The methods used to estimate a property of a population on the basis of a sample.page 6 Inferential statistics is widely applied to learn something about a population in business, agriculture, politics, and government, as shown in the following examples:Television networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers. During the week of December 3, 2018, The Tonight Show Starring Jimmy Fallon was viewed by 2.26 million people in the 18–49 age. The Late Show with Stephen Colbert led the age group with 3.23 million viewers (https://tvbythenumbers.zap2it.com/tag/jimmy-kimmel-live-ratings/). These program ratings are used to make decisions about advertising rates and whether to continue or cancel a program.In 2015, a sample of U.S. Internal Revenue Service tax preparation volunteers were tested with three standard tax returns. The sample indicated that tax returns were completed with a 49% accuracy rate. In other words there were errors on about half of the returns. In this example, the statistics are used to make decisions about how to improve the accuracy rate by correcting the most common errors and improving the training of volunteers.A feature of our text is self-review problems. There are a number of them interspersed throughout each chapter. The first self-review follows. Each self-review tests your comprehension of preceding material. The answer and method of solution are given in Appendix D. You can find the answer to the following self-review in 1–1 in Appendix D. We recommend that you solve each one and then check your answer.SELF-REVIEW 1–1The answers are in Appendix D.The Atlanta-based advertising firm Brandon and Associates asked a sample of 1,960 consumers to try a newly developed chicken dinner by Boston Market. Of the 1,960 sampled, 1,176 said they would purchase the dinner if it is marketed.(a) Is this an example of descriptive statistics or inferential statistics? Explain.(b) What could Brandon and Associates report to Boston Market regarding acceptance of the chicken dinner in the population?

Distinguish among nominal, ordinal, interval, and ratio levels of measurement.Data can be classified according to levels of measurement. The level of measurement determines how data should be summarized and presented. It also will indicate the type of statistical analysis that can be performed. Here are two examples of the relationship between measurement and how we apply statistics. There are six colors of candies in a bag of M&Ms. Suppose we assign brown a value of 1, yellow 2, blue 3, orange 4, green 5, and red 6. What kind of variable is the color of an M&M? It is a qualitative variable. Suppose someone summarizes M&M color by adding the assigned color values, divides the sum by the number of M&Ms, and reports that the mean color is 3.56. How do we interpret this statistic? You are correct in concluding that it has no meaning as a measure of M&M color. As a qualitative variable, we can only report the count and percentage of each color in a bag of M&Ms. As a second example, in a high school track meet there are eight competitors in the 400-meter run. We report the order of finish and that the mean finish is 4.5. What does the mean finish tell us? Nothing! In both of these instances, we have not used the appropriate statistics for the level of measurement.Ron Buskirk/Alamy Stock PhotoThere are four levels of measurement: nominal, ordinal, interval, and ratio. The lowest, or the most primitive, measurement is the nominal level. The highest is the ratio level of measurement.Nominal-Level DataFor the nominal level of measurement, observations of a qualitative variable are measured and recorded as labels or names. The labels or names can only be classified and counted. There is no particular order to the labels.page 8 NOMINAL LEVEL OF MEASUREMENT Data recorded at the nominal level of measurement is represented as labels or names. They have no order. They can only be classified and counted.A classification of M&M candies based on their color is an example of the nominal level of measurement. We simply classify the candies by color. There is no natural order. That is, we could report the brown candies first, the orange first, or any of the other colors first. Recording the variable gender is another example of the nominal level of measurement. Suppose we count the number of students entering a football game with a student ID and report how many are men and how many are women. We could report either the men or the women first. For the data measured at the nominal level, we are limited to counting the number in each category of the variable. Often, we convert these counts to percentages. For example, a random sample of M&M candies reports the following percentages for each color:Color Percent in a bagBlue 24%Green 20%Orange 16%Yellow 14%Red 13%Brown 13%To process the data for a variable measured at the nominal level, we often numerically code the labels or names. For example, if we are interested in measuring the home state for students at East Carolina University, we would assign a student’s home state of Alabama a code of 1, Alaska a code of 2, Arizona a 3, and so on. Using this procedure with an alphabetical listing of states, Wisconsin is coded 49 and Wyoming 50. Realize that the number assigned to each state is still a label or name. The reason we assign numerical codes is to facilitate counting the number of students from each state with statistical software. Note that assigning numbers to the states does not give us license to manipulate the codes as numerical information. Specifically, in this example, 1 + 2 = 3 corresponds to Alabama + Alaska = Arizona. Clearly, the nominal level of measurement does not permit any mathematical operation that has any valid interpretation.Ordinal-Level DataThe next higher level of measurement is the ordinal level. For this level of measurement a qualitative variable or attribute is either ranked or rated on a relative scale.ORDINAL LEVEL OF MEASUREMENT Data recorded at the ordinal level of measurement is based on a relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked or counted.Best Business ClimateAlabamaTexasTennesseeUtahVirginaSouth CarolinaIndianaFloridaNevadaMississippiFor example, many businesses make decisions about where to locate their facilities; in other words, where is the best place for their business? Business Facilities (Search “Rankings” at https://businessfacilities.com/) publishes a list of the top 10 states for the “best business climate.” The 2018 rankings are shown to the left. They are based on the evaluation of many different factors, including the cost of labor, business tax climate, quality of life, transportation infrastructure, educated workforce, and economic growth potential.page 9 This is an example of an ordinal scale because the states are ranked in order of best to worst business climate. That is, we know the relative order of the states based on the attribute. For example, in 2018 Alabama had the best business climate and Texas was second. Virginia was fifth, and that was better than South Carolina but not as good as Utah. We cannot say that Alabama’s business climate is five times better than Virgina’s business climate because the magnitude of the difference between the states is not known. To put it another way, we do not know if the magnitude of the difference between Alabama and Texas is the same as between Tennessee and Utah.Another example of the ordinal level measure is based on a scale that measures an attribute. This type of scale is used when students rate instructors on a variety of attributes. One attribute may be: “Overall, how do you rate the quality of instruction in this class?” A student’s response is recorded on a relative scale of inferior, poor, good, excellent, and superior. An important characteristic of using a relative measurement scale is that we cannot distinguish the magnitude of the differences between the responses. We do not know if the difference between “Superior” and “Good” is the same as the difference between “Poor” and “Inferior.”Table 1–1 lists the frequencies of 60 student ratings of instructional quality for Professor James Brunner in an Introduction to Finance course. The data are summarized based on the order of the scale used to rate the instructor. That is, they are summarized by the number of students who indicated a rating of superior (6), good (26), and so on. We also can convert the frequencies to percentages. About 43.3% (26/60) of the students rated the instructor as good.TABLE 1–1 Rating of a Finance ProfessorRating Frequency PercentageSuperior  6 10.0%Good 26 43.3%Average 16 26.7%Poor  9 15.0%Inferior  3  5.0%Interval-Level DataThe interval level of measurement is the next highest level. It includes all the characteristics of the ordinal level, but, in addition, the difference or interval between values is meaningful.INTERVAL LEVEL OF MEASUREMENT For data recorded at the interval level of measurement, the interval or the distance between values is meaningful. The interval level of measurement is based on a scale with a known unit of measurement.The Fahrenheit temperature scale is an example of the interval level of measurement. Suppose the high temperatures on three consecutive winter days in Boston are 28, 31, and 20 degrees Fahrenheit. These temperatures can be easily ranked, but we can also determine the interval or distance between temperatures. This is possible because 1 degree Fahrenheit represents a constant unit of measurement. That is, the distance between 10 and 15 degrees Fahrenheit is 5 degrees, and is the same as the 5-degree distance between 50 and 55 degrees Fahrenheit. It is also important to note that 0 is just a point on the scale. It does not represent the absence of the condition. The measurement of zero degrees Fahrenheit does not represent the absence of heat or cold. But by our own measurement scale, it is cold! A major limitation of a variable measured at the interval level is that we cannot make statements similar to 20 degrees Fahrenheit is twice as warm as 10 degrees Fahrenheit.page 10 Another example of the interval scale of measurement is women’s dress sizes. Listed below is information on several dimensions of a standard U.S. woman’s dress.Size Bust (in) Waist (in) Hips (in) 8 32 24 3510 34 26 3712 36 28 3914 38 30 4116 40 32 4318 42 34 4520 44 36 4722 46 38 4924 48 40 5126 50 42 5328 52 44 55Why is the “size” scale an interval measurement? Observe that as the size changes by two units (say from size 10 to size 12 or from size 24 to size 26), each of the measurements increases by 2 inches. To put it another way, the intervals are the same.There is no natural zero point for dress size. A “size 0” dress does not have “zero” material. Instead, it would have a 24-inch bust, 16-inch waist, and 27-inch hips. Moreover, the ratios are not reasonable. If you divide a size 28 by a size 14, you do not get the same answer as dividing a size 20 by a size 10. Neither ratio is equal to two, as the “size” number would suggest. In short, if the distances between the numbers make sense, but the ratios do not, then you have an interval scale of measurement.Ratio-Level DataAlmost all quantitative variables are recorded on the ratio level of measurement. The ratio level is the “highest” level of measurement. It has all the characteristics of the interval level, but, in addition, the 0 point and the ratio between two numbers are both meaningful.RATIO LEVEL OF MEASUREMENT Data recorded at the ratio level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale.Examples of the ratio scale of measurement include wages, units of production, weight, changes in stock prices, distance between branch offices, and height. Money is also a good illustration. If you have zero dollars, then you have no money, and a wage of $50 per hour is two times the wage of $25 per hour. Weight also is measured at the ratio level of measurement. If a scale is correctly calibrated, then it will read 0 when nothing is on the scale. Further, something that weighs 1 pound is half as heavy as something that weighs 2 pounds.Table 1–2 illustrates the ratio scale of measurement for the variable, annual income for four father-and-son combinations. Observe that the senior Lahey earns twice as much as his son. In the Rho family, the son makes twice as much as the father.TABLE 1–2 Father–Son Income CombinationsName Father SonLahey $80,000 $ 40,000Nale  90,000   30,000Rho  60,000  120,000Steele  75,000  130,000Chart 1–3 summarizes the major characteristics of the various levels of measurement. The level of measurement will determine the type of statistical methods that can be used to analyze a variable. Statistical methods to analyze variables measured on a nominal level are discussed in Chapter 15; methods for ordinal-level variables are discussed in Chapter 16. Statistical methods to analyze variables measured on an interval or ratio level are presented in Chapters 9 through 14.page 11 CHART 1–3 Summary and Examples of the Characteristics for Levels of MeasurementSELF-REVIEW 1–2(a) The mean age of people who listen to talk radio is 42.1 years. What level of measurement is used to assess the variable age?(b) In a survey of luxury-car owners, 8% of the U.S. population own luxury cars. In California and Georgia, 14% of people own luxury cars. Two variables are included in this information. What are they and how are they measured?EXERCISESThe answers to the odd-numbered exercises are in Appendix C.What is the level of measurement for each of the following variables?Student IQ ratings.Distance students travel to class.The jersey numbers of a sorority soccer team.A student’s state of birth.A student’s academic class—that is, freshman, sophomore, junior, or senior.Number of hours students study per week.Slate is a daily magazine on the Web. Its business activities can be described by a number of variables. What is the level of measurement for each of the following variables?The number of hits on their website on Saturday between 8:00 a.m. and 9:00 a.m.The departments, such as food and drink, politics, foreign policy, sports, etc.The number of weekly hits on the Sam’s Club ad.The number of years each employee has been employed with Slate.On the Web, go to your favorite news source and find examples of each type of variable. Write a brief memo that lists the variables and describes them in terms of qualitative or quantitative, discrete or continuous, and the measurement level.For each of the following, determine whether the group is a sample or a population.The participants in a study of a new cholesterol drug.The drivers who received a speeding ticket in Kansas City last month.People on welfare in Cook County (Chicago), Illinois.The 30 stocks that make up the Dow Jones Industrial Average.page 12

LO2-1Summarize qualitative variables with frequency and relative frequency tables.Recall from Chapter 1 that techniques used to describe a set of data are called descriptive statistics. Descriptive statistics organize data to show the general pattern of the data, to identify where values tend to concentrate, and to expose extreme or unusual data values. The first technique we discuss is a frequency table.FREQUENCY TABLE A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.page 20 In Chapter 1, we distinguished between qualitative and quantitative variables. To review, a qualitative variable is nonnumeric, that is, it can only be classified into distinct categories. Examples of qualitative data include political affiliation (Republican, Democrat, Independent, or other), state of birth (Alabama, . . ., Wyoming), and method of payment for a purchase at Barnes & Noble (cash, digital wallet, debit, or credit). On the other hand, quantitative variables are numerical in nature. Examples of quantitative data relating to college students include the price of their textbooks, their age, and the number of credit hours they are registered for this semester.In the Applewood Auto Group data set, there are five variables for each vehicle sale: age of the buyer, amount of profit, dealership that made the sale, type of vehicle sold, and number of previous purchases by the buyer. The dealership and the type of vehicle are qualitative variables. The amount of profit, the age of the buyer, and the number of previous purchases are quantitative variables.Image Source, all rights reserved.Suppose Ms. Ball wants to summarize last month’s sales by location. The first step is to sort the vehicles sold last month according to their location and then tally, or count, the number sold at each of the four locations: Tionesta, Olean, Sheffield, or Kane. The four locations are used to develop a frequency table with four mutually exclusive (distinctive) classes. Mutually exclusive classes means that a particular vehicle can be assigned to only one class. In addition, the frequency table must be collectively exhaustive. That is, every vehicle sold last month is accounted for in the table. If every vehicle is included in the frequency table, the table will be collectively exhaustive and the total number of vehicles will be 180. How do we obtain these counts? Excel provides a tool called a Pivot Table that will quickly and accurately establish the four classes and do the counting. The Excel results follow in Table 2–1. The table shows a total of 180 vehicles; of the 180 vehicles, 52 were sold at Kane Motors.TABLE 2–1 Frequency Table for Vehicles Sold Last Month at Applewood Auto Group by LocationLocation Number of CarsKane  52Olean  40Sheffield  45Tionesta  43Total 180Relative Class FrequenciesYou can convert class frequencies to relative class frequencies to show the fraction of the total number of observations in each class. A relative frequency captures the relationship between a class frequency and the total number of observations. In the vehicle sales example, we may want to know the percentage of total cars sold at each of the four locations. To convert a frequency table to a relative frequency table, each of the class frequencies is divided by the total number of observations. Again, this is easily accomplished using Excel. The fraction of vehicles sold last month at the Kane location is 0.289, found by 52 divided by 180. The relative frequency for each location is shown in Table 2–2.TABLE 2–2 Relative Frequency Table of Vehicles Sold by Location Last Month at Applewood Auto GroupLocation Number of Cars Relative Frequency Found byKane  52  .289 52/180Olean  40  .222 40/180Sheffield  45  .250 45/180Tionesta  43  .239 43/180Total 180 1.000  page 21 Graphic Presentation of Qualitative DataLO2-2Display a frequency table using a bar or pie chart.The most common graphic form to present a qualitative variable is a bar chart. In most cases, the horizontal axis shows the variable of interest. The vertical axis shows the frequency or fraction of each of the possible outcomes. A distinguishing feature of a bar chart is there is distance or a gap between the bars. That is, because the variable of interest is qualitative, the bars are not adjacent to each other. Thus, a bar chart graphically describes a frequency table using a series of uniformly wide rectangles, where the height of each rectangle is the class frequency.BAR CHART A graph that shows qualitative classes on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.We use the Applewood Auto Group data as an example (Chart 2–1). The variables of interest are the location where the vehicle was sold and the number of vehicles sold at each location. We label the horizontal axis with the four locations and scale the vertical axis with the number sold. The variable location is of nominal scale, so the order of the locations on the horizontal axis does not matter. In Chart 2–1, the locations are listed alphabetically. The locations also could be in order of decreasing or increasing frequencies.CHART 2–1 Number of Vehicles Sold by LocationThe height of the bars, or rectangles, corresponds to the number of vehicles at each location. There were 52 vehicles sold last month at the Kane location, so the height of the Kane bar is 52; the height of the bar for the Olean location is 40. See link to a tutorial showing how to create a vertical bar chart in Excel.Tutorial #3 in ConnectAnother useful type of chart for depicting qualitative information is a pie chart.PIE CHART A chart that shows the proportion or percentage that each class represents of the total number of frequencies.We explain the details of constructing a pie chart using the information in Table 2–3, which shows the frequency and percent of cars sold by the Applewood Auto Group for each vehicle type.page 22 TABLE 2–3 Vehicle Sales by Type at Applewood Auto GroupVehicle Type Number Sold Percent SoldSedan  72  40SUV  54  30Compact  27  15Truck  18  10Hybrid  9  5Total 180 100The first step to develop a pie chart is to mark the percentages 0, 5, 10, 15, and so on evenly around the circumference of a circle (see Chart 2–2). To plot the 40% of total sales represented by sedans, draw a line from the center of the circle to 0 and another line from the center of the circle to 40%. The area in this “slice” represents the number of sedans sold as a percentage of the total sales. Next, add the SUV’s percentage of total sales, 30%, to the sedan’s percentage of total sales, 40%. The result is 70%. Draw a line from the center of the circle to 70%, so the area between 40 and 70 shows the sales of SUVs as a percentage of total sales. Continuing, add the 15% of total sales for compact vehicles, which gives us a total of 85%. Draw a line from the center of the circle to 85, so the “slice” between 70% and 85% represents the number of compact vehicles sold as a percentage of the total sales. The remaining 10% for truck sales and 5% for hybrid sales are added to the chart using the same method. See link in the margin to a tutorial showing how to create a pie chart in Excel.CHART 2–2 Pie Chart of Vehicles by TypeTutorial #4 in ConnectBecause each slice of the pie represents the relative frequency of each vehicle type as a percentage of the total sales, we can easily compare them:The largest percentage of sales is sedans.Sedans and SUVs together account for 70% of vehicle sales.Hybrids account for 5% of vehicle sales.We can use Excel software to quickly count the number of cars for each vehicle type and create the frequency table, bar chart, and pie chart shown in the following summary. The Excel tool is called a Pivot Table. The instructions to produce these descriptive statistics and charts are provided in the Excel tutorials. See the link in the margin. The Applewood data set is available in Connect.Tutorial #7 in Connectpage 23 Source: Microsoft ExcelPie and bar charts both serve to illustrate frequency and relative frequency tables. When is a pie chart preferred to a bar chart? In most cases, pie charts are used to show and compare the relative differences in the percentage of observations for each value or class of a qualitative variable. Bar charts are preferred when the goal is to compare the number or frequency of observations for each value or class of a qualitative variable. The following Example/Solution shows another application of bar and pie charts. EXAMPLESkiLodges.com is test marketing its new website and is interested in how easy its website design is to navigate. The Analytics Department at SkiLodges.com randomly selected 200 regular Internet users and asked them to perform a search task on the website. Each person was asked to rate the relative ease of navigation as poor, good, excellent, or awesome. The results are shown in the following table:Awesome 102Excellent  58Good  30Poor  10What type of measurement scale is used for ease of navigation?Draw a bar chart for the survey results.Draw a pie chart for the survey results.SOLUTIONThe data are measured on an ordinal scale. That is, the scale is ranked in relative ease of navigation when moving from “awesome” to “poor.” The interval between each rating is unknown so it is impossible, for example, to conclude that a rating of good is twice the value of a poor rating.We can use a bar chart to graph the data. The vertical scale shows the relative frequency and the horizontal scale shows the values of the ease-of-navigation variable.page 24 A pie chart also can be used to graph these data. The pie chart emphasizes that more than half of the respondents rate the relative ease of using the website awesome.SELF-REVIEW 2–1The answers are in Appendix D.DeCenzo Specialty Food and Beverage Company has been serving a cola drink with an additional flavoring, Cola-Plus, that is very popular among its customers. The company is interested in customer preferences for Cola-Plus versus Coca-Cola, Pepsi, and a lemon-lime beverage. They ask 100 randomly sampled customers to take a taste test and select the beverage they prefer most. The results are shown in the following table:Beverage NumberCola-Plus  40Coca-Cola  25Pepsi  20Lemon-Lime  15Total 100page 25 (a) Are the data qualitative or quantitative? Why?(b) What is the table called? What does it show?(c) Develop a bar chart to depict the information.(d) Develop a pie chart using the relative frequencies.EXERCISESThe answers to the odd-numbered exercises are at the end of the book in Appendix C.A pie chart shows the relative market share of cola products. The “slice” for Pepsi has a central angle of 90 degrees. What is its market share?In a marketing study, 100 consumers were asked to select the best digital music player from the iPod Touch, Sony Walkman, and the Zune HD. To summarize the consumer responses with a frequency table, how many classes would the frequency table have?A total of 1,000 residents in Minnesota were asked which season they preferred. One hundred liked winter best, 300 liked spring, 400 liked summer, and 200 liked fall. Develop a frequency table and a relative frequency table to summarize this information.Two thousand frequent business travelers were asked which midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. One hundred liked Indianapolis best, 450 liked Saint Louis, 1,300 liked Chicago, and the remainder preferred Milwaukee. Develop a frequency table and a relative frequency table to summarize this information.Wellstone Inc. produces and markets replacement covers for cell phones in five different colors: bright white, metallic black, magnetic lime, tangerine orange, and fusion red. To estimate the demand for each color, the company set up a kiosk for several hours in the Mall of America and asked randomly selected people which cover color was their favorite. The results follow:Bright white 130Metallic black 104Magnetic lime 325Tangerine orange 455Fusion red 286What is the table called?Draw a bar chart for the table.Draw a pie chart.If Wellstone Inc. plans to produce 1 million cell phone covers, how many of each color should it produce?A small business consultant is investigating the performance of several companies. The fourth-quarter sales for last year (in thousands of dollars) for the selected companies were:Company Fourth-Quarter Sales($ thousands)Hoden Building Products $ 1,645.2J & R Printing Inc.  4,757.0Long Bay Concrete Construction  8,913.0Mancell Electric and Plumbing    627.1Maxwell Heating and Air Conditioning  24,612.0Mizelle Roofing & Sheet Metals   191.9The 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.page 26