WIXLIB

Essentials of Modern Business Statistics (7e)Pareto Diagram In quality control, bar charts are used to identify the mostimportant causes of problems. When the bars are arranged in descending order of height from leftto right (with the most frequently occurring cause appearing first)the bar chart is called a Pareto diagram. This diagram is named for its founder, Vilfredo Pareto, an Italianeconomist. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.19

Essentials of Modern Business Statistics (7e)Pie Chart The pie chart is a commonly used graphical display for presentingrelative frequency and percent frequency distributions forcategorical data. First draw a circle; then use the relative frequencies to subdividethe circle into sectors that correspond to the relative frequency foreach class. Since there are 360 degrees in a circle, a class with a relativefrequency of .25 would consume .25(360) 90 degrees of the circle. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.20

Essentials of Modern Business Statistics (7e)Pie ChartSprite5%Coca-Cola10%Diet Coke15%Coca-ColaDiet CokeDr. PepperPepsi45%PepsiSpriteDr. Pepper25% 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.21

Essentials of Modern Business Statistics (7e)Pie ChartExampleInferences from the Pie Chart Almost one-half of the customers surveyed preferred Pepsi(looking at the left side of the pie). The second preference is for Dr. Pepper with 25% of thecustomers opting for it. Only 5% of the customers opted for Sprite. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.22

Essentials of Modern Business Statistics (7e)Using Excel’s Recommended Charts Toolto Construct a Pie Chart To display a pie chart, click anywhere in the bar chart to displaythree tabs (Analyze, Design, and Format) located on the ribbonunder the heading PivotChart Tools. Click the Design tab and choose the Change Chart Type option todisplay the Change Chart Type dialog box. Click the Pie option and then OK. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.23

Essentials of Modern Business Statistics (7e)Using Excel’s Recommended Charts Toolto Construct a Pie Chart 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.24

Essentials of Modern Business Statistics (7e)Summarizing Quantitative Data Frequency Distribution Relative Frequency and Percent Frequency Distributions Dot Plot Histogram Cumulative Distributions Stem-and-Leaf Display 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.25

Essentials of Modern Business Statistics (7e)Frequency DistributionExampleSanderson and Clifford, a small public accounting firm wants todetermine time in days required to complete year end audits. It takes asample of 20 clients. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.26

Essentials of Modern Business Statistics (7e)Frequency DistributionExample: Sanderson and CliffordYear-end Audit Time (in Days)1215202214141527211819182233161817232813 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.27

Essentials of Modern Business Statistics (7e)Frequency DistributionThe three steps necessary to define the classes for a frequencydistribution with quantitative data are: Step 1 - Determine the number of non-overlappingclasses. Step 2 - Determine the width of each class. Step 3 - Determine the class limits. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.28

Essentials of Modern Business Statistics (7e)Frequency DistributionGuidelines for Determining the Number of Classes Use between 5 and 20 classes. Data sets with a larger number of elements usually require a largernumber of classes. Smaller data sets usually require fewer classes. The goal is to use enough classes to show the variation in the data, butnot so many classes that some contain only a few data items. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.29

Essentials of Modern Business Statistics (7e)Frequency DistributionGuidelines for Determining the Width of Each Class Use classes of equal width. Approximate Class Width Making the classes the same width reduces the chance ofinappropriate interpretations. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.30

Essentials of Modern Business Statistics (7e)Frequency Distribution Note on Number of Classes and Class WidthIn practice, the number of classes and the appropriate class widthare determined by trial and error.Once a possible number of classes is chosen, the appropriate classwidth is found.The process can be repeated for a different number of classes.Ultimately, the analyst uses judgment to determine the combinationof the number of classes and class width that provides the bestfrequency distribution for summarizing the data. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.31

Essentials of Modern Business Statistics (7e)Frequency Distribution Guidelines for Determining the Class LimitsClass limits must be chosen so that each data item belongs to oneand only one class.The lower class limit identifies the smallest possible data valueassigned to the class.The upper class limit identifies the largest possible data valueassigned to the class.The appropriate values for the class limits depend on the level ofaccuracy of the data.An open-end class requires only a lower class limit or an upper classlimit. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.32

Essentials of Modern Business Statistics (7e)Frequency DistributionClass Midpoint In some cases, we want to know the midpoints of the classes in afrequency distribution for quantitative data. The class midpoint is the value halfway between the lower andupper class limits. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.33

Essentials of Modern Business Statistics (7e)Frequency DistributionExample: Sanderson and Clifford If we choose five classes: Approximate Class Width (33 - 12)/5 4.2 4Time in daysFrequency10-14415-19820-24525-29230-341Total20 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.34

Essentials of Modern Business Statistics (7e)Using Excel’s PivotTableto Construct a Frequency Distribution Step 1 – Select any cell in the data set Step 2 – Click Insert on the Ribbon Step 3 – In the Tables group click Pivot Table Step 4 - When the Create PivotTable dialog box appears: Click(a PivotTable and PivotTable Fields dialog box will appear in anew worksheet) 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.35

Essentials of Modern Business Statistics (7e)Using Excel’s PivotTableto Construct a Frequency Distribution Step 5 - In the PivotTable Fields dialog box:Drag Audit time to the Rows areaDrag Audit time to the Values area Step 6 - Click on Sum of Audit time in the Values area Step 7 - Click Value Field Settings from the list of options Step 8 - When the Value Field Settings dialog box appears: UnderSummarize value field by, choose Count Click OK 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.36

Essentials of Modern Business Statistics (7e)Using Excel’s PivotTableto Construct a Frequency DistributionTo construct the frequency distribution, we must group the rows containingaudit time. Step 1 - Right click any cell in the PivotTable reportcontaining a an audit time. Step 2 - Choose Group from the list of options that appears Step 3 - When the Grouping dialog box appears: Enter 10 in the Starting at box Enter 34 in the Ending at box Enter 5 in the By box Click OK 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.37

Essentials of Modern Business Statistics (7e)Using Excel’s Pivot table to constructa frequency distribution 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.38

Essentials of Modern Business Statistics (7e)Relative Frequency and Percent Frequency DistributionsExample: Sanderson and CliffordAudit time(in days)Relative FrequencyPercent Frequency10 – 14.20 (4/20)20 (0.2 * 100)15 – 19.404020 – 25.252525 – 29.101030 – 34.055Total 1.00100 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.39

Essentials of Modern Business Statistics (7e)Relative Frequency and Percent FrequencyDistributionsExample: Sanderson and CliffordInsights obtained from the Percent Frequency Distribution: 40% of the audits required from 15 to 19 days. Another 25% of the audits required 20 to 25 days. Only 5% of the audits required more than 30 days. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.40

Essentials of Modern Business Statistics (7e)Dot Plot One of the simplest graphical summaries of data is a dot plot. A horizontal axis shows the range of data values. Then each data value is represented by a dot placed above the axis. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.41

Essentials of Modern Business Statistics (7e)Dot PlotExample: Sanderson and Clifford 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.42

Essentials of Modern Business Statistics (7e)Histogram Another common graphical display of quantitative data is ahistogram. The variable of interest is placed on the horizontal axis. A rectangle is drawn above each class interval with its heightcorresponding to the interval’s frequency, relative frequency, orpercent frequency. Unlike a bar graph, a histogram has no natural separation betweenrectangles of adjacent classes. 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.43

Essentials of Modern Business Statistics (7e)HistogramExample: Sanderson and Clifford 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.44

Essentials of Modern Business Statistics (7e)Using Excel’s Recommended Charts Toolto Construct a Histogram Step 1 - Select any cell in the PivotTable report Step 2 - Click Insert on the Ribbon Step 3 - In the Charts group, click Recommended Charts Step 4 - Click OK editing options 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.45

Essentials of Modern Business Statistics (7e)Using Excel’s Recommended Charts Toolto Construct a Histogram Step 1 – Right-click any bar in the chart and chooseFormat Data Series from the list of options Step 2 - When the Format Data Series dialog box appears:Go to the Series Options sectionSet the Gap Width to 0Click the Close button at the top right Step 3 - Click the Chart Title and replace it with Audit time data Step 4 - Click the Chart Elements button (in top right corner of the chart) 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service orotherwise on a password-protected website or school-approved learning management system for classroom use.46

Essentials of Modern Business Statistics (7e)Using Excel’s Recommended Charts Toolto Construct a Histogram Step 5 – When the list

Essentials of Modern Business Statistics (7e) A frequency distribution is a tabular summary of data showing the number (frequency) of observations in each of several non-overlapping categories or classes. The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.