Business Statistics- A Decision-Making Approach

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-1Business Statistics: A Decision-Making Approach6thEditionChapter 2Graphs, Charts, and Tables –Describing Your DataBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-2Chapter GoalsAfter completing this chapter, you should be able to:Construct a frequency distribution both manually and with a computerConstruct and interpret a histogramCreate and interpret bar charts, pie charts, and stem-and-leaf diagramsPresent and interpret data in line charts and scatter diagramsBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-3Frequency DistributionsWhat is a Frequency Distribution?A frequency distribution is a list or a table…containing the values of a variable(or a set of ranges within which the data fall) ...and the corresponding frequencieswith which each value occurs (or frequencies with which data fall within each range)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-4Why Use Frequency Distributions?A frequency distribution is a way to summarize dataThe distribution condenses the raw data into a more useful form... and allows for a quick visual interpretation of the dataBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-5Frequency Distribution: Discrete DataDiscrete data:possible values are countableExample:An advertiser asks 200 customers how many days per week they read the daily newspaper.Number of days readFrequency044124218316420522626730Total200Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-6Relative FrequencyRelative Frequency: What proportion is in each category?Number of days readFrequencyRelativeFrequency044.22124.12218.09316.08420.10522.11626.13730.15Total2001.00.222004422% of the people in the sample report that they read the newspaper 0 days per weekBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-7Frequency Distribution: Continuous DataContinuous Data:may take on any value in some intervalExample:A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27(Temperature is a continuous variable because it could be measured to any degree of precision desired)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-8Grouping Data by ClassesSort raw data in ascending order:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Find range: 58 -12 = 46Select number of classes: 5(usually between 5 and 20)Compute class width: 10(46/5 then round off)Determine class boundaries:10, 20, 30, 40, 50Compute class midpoints: 15, 25, 35, 45, 55Count observations & assign to classesBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-9Frequency Distribution ExampleData in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58ClassFrequency10 but under 20 3 .15 20 but under 306 .30 30 but under 405 .25 40 but under 50 4 .20 50 but under 602 .10 Total20 1.00RelativeFrequencyFrequency DistributionBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-10HistogramsThe classesorintervalsare shown on the horizontal axisfrequencyis measured on the vertical axisBars of the appropriate heights can be used to represent the number of observations within each class Such a graph is called a histogramBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-11Histogram03654200123456751525364555MoreFrequencyClass MidpointsHistogram ExampleData in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58No gaps between bars, since continuous dataBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-12Questions for Grouping Data into Classes1.How wide should each interval be?(How many classes should be used?)2.How should the endpoints of theintervals be determined?Often answered by trial and error, subject to user judgmentThe goal is to create a distribution that is neither too "jagged" nor too "blocky” Goal is to appropriately show the pattern of variation in the dataBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-13How Many Class Intervals?Many (Narrow class intervals)may yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classesFew (Wide class intervals)may compress variation too much and yield a blocky distributioncan obscure important patterns of variation.02468101203060MoreTemperatureFrequency00.511.522.533.54812162024283236404448525660MoreTemperatureFrequency(X axis labels are upper class endpoints)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-14General GuidelinesNumber of Data Points Number of Classesunder 50 5 -7 50 –100 6 -10100 –250 7 -12over 250 10 -20Class widths can typically be reduced as the number of observations increasesDistributions with numerous observations are more likely to be smooth and have gaps filled since data are plentifulBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-15Class WidthThe class width is the distance between the lowest possible value and the highest possible value for a frequency classThe minimum class width isLargest Value -Smallest ValueNumber of ClassesW =Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-16Histograms in ExcelSelectTools/Data Analysis1Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-17Choose Histogram23Input data and bin rangesSelect Chart OutputHistograms in Excel(continued)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-18Stem and Leaf DiagramA simple way to see distribution details in a data setMETHOD: Separate the sorted data seriesinto leading digits (the stem) andthe trailing digits (theleaves)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-19Example:Here, use the 10’s digit for the stem unit:Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 5812 is shown as35 is shown asStem Leaf1 23 5Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-20Example:Completed Stem-and-leaf diagram:Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58StemLeaves12 3 721 4 4 6 7 830 2 5 7 841 3 4 653 8Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-21Using other stem unitsUsing the 100’s digit as the stem:Round off the 10’s digit to form the leaves613 would become 6 1776 would become 7 8. . .1224 becomes 12 2Stem LeafBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-22Graphing Categorical DataCategorical DataPie ChartsPareto DiagramBar ChartsBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-23Bar and Pie ChartsBar charts and Pie charts are often used for qualitative (category) dataHeight of bar or size of pie slice shows the frequency or percentage for each categoryBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-24Pie Chart ExamplePercentages are rounded to the nearest percentCurrent Investment Portfolio Savings 15%CD 14%Bonds 29%Stocks42%Investment Amount PercentageType(in thousands $)Stocks 46.5 42.27Bonds32.0 29.09CD15.5 14.09Savings 16.0 14.55Total110100(Variables are Qualitative)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-25Bar Chart ExampleInvestor's Portfolio01020304050StocksBondsCDSavingsAmount in $1000'sBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-26Pareto Diagram Examplecumulative % invested (line graph)% invested in each category (bar graph)0%5%10%15%20%25%30%35%40%45%StocksBondsSavingsCD0%10%20%30%40%50%60%70%80%90%100%Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-27Bar Chart ExampleNewspaper readership per week0102030405001234567Number of days newspaper is read per weekFreuencyNumber of days readFrequency044124218316420522626730Total200Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-28Tabulating and Graphing Multivariate Categorical DataInvestment in thousands of dollarsInvestment Investor A Investor BInvestor CTotal CategoryStocks46.55527.5129Bonds32.0 4419.0 95CD15.5 20 13.5 49Savings16.028 7.0 51Total110.0147 67.0324Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-29Tabulating and Graphing Multivariate Categorical DataSide by side chartsComparing Investors0102030405060StocksBondsCDSavingsInvestor AInvestor BInvestor C(continued)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-30Side-by-Side Chart ExampleSales by quarter for three sales territories:01020304050601st Qtr2nd Qtr3rd Qtr4th QtrEastWestNorth1st Qtr2nd Qtr3rd Qtr4th QtrEast20.427.45920.4West30.638.634.631.6North45.946.94543.9Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-31Line chartsshow values of one variable vs. timeTime is traditionally shown on the horizontal axisScatter Diagramsshow points for bivariate data one variable is measured on the vertical axis and the other variable is measured on the horizontal axisLine Charts and Scatter DiagramsBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-32Line Chart ExampleU.S. Inflation Rate01234561984198619881990199219941996199820002002YearInflation Rate (%)YearInflation Rate19853.5619861.8619873.6519884.1419894.8219905.4019914.2119923.0119932.9919942.5619952.8319962.9519972.2919981.5619992.2120003.3620012.8520021.58Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-33Scatter Diagram ExampleProduction Volume vs. Cost per Day050100150200250010203040506070Volume per DayCost per Day Volume per dayCost per day231252614029146331603816742170501885519560200Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-34Types of RelationshipsLinear RelationshipsXXYYBusiness Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-35Curvilinear RelationshipsXXYYTypes of Relationships(continued)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-36No RelationshipXXYYTypes of Relationships(continued)Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.Chap 2-37Chapter SummaryData in raw form are usually not easy to use for decision making --Some type of organization is needed:TableGraphTechniques reviewed in this chapter:Frequency Distributions and HistogramsBar Charts and Pie ChartsStem and Leaf DiagramsLine Charts and Scatter Diagrams