ch02a - Chapter 2 Descriptive Statistics: Tabular and...

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Unformatted text preview: Chapter 2 Descriptive Statistics: Tabular and Graphical Methods Part A s s Summarizing Qualitative Data Summarizing Quantitative Data Slide 1 Summarizing Qualitative Data s s s s s Frequency Distribution Relative Frequency Distribution Percent Frequency Distribution Bar Graph Pie Chart Slide 2 Frequency Distribution A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several nonoverlapping classes. The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data. Slide 3 Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: Above Average Above Average Average Above Average Average Above Average Below Average Average Above Average Below Average Poor Excellent Above Average Average Above Average Above Average Below Average Poor Above Average Average Average Slide 4 Frequency Distribution Rating Frequency 2 Poor 3 Below Average 5 Average 9 Above Average 1 Excellent Total 20 Slide 5 Using Excel's COUNTIF Function to Construct a Frequency Distribution s Formula Worksheet A Quality Rating Above Average Below Average Above Average Average Average Above Average Above Average B C Quality Rating Poor Below Average Average Above Average Excellent Total D Frequency =COUNTIF($A$2:$A$21,C2) =COUNTIF($A$2:$A$21,C3) =COUNTIF($A$2:$A$21,C4) =COUNTIF($A$2:$A$21,C5) =COUNTIF($A$2:$A$21,C6) =SUM(D2:D6) 1 2 3 4 5 6 7 8 Note: Rows 921 are not shown. Slide 6 Using Excel's COUNTIF Function to Construct a Frequency Distribution s Value Worksheet A Quality Rating Above Average Below Average Above Average Average Average Above Average Above Average B C Quality Rating Poor Below Average Average Above Average Excellent Total D Frequency 2 3 5 9 1 20 1 2 3 4 5 6 7 8 Note: Rows 921 are not shown. Slide 7 Relative Frequency Distribution The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. Slide 8 Percent Frequency Distribution The percent frequency of a class is the relative frequency multiplied by 100. A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class. Slide 9 Relative Frequency and Percent Frequency Distributions Relative Frequency Rating .10 Poor .15 Below Average .25 Average .45 Above Average .05 Excellent Total 1.00 Percent Frequency 10 15 25 .10(100) = 10 45 5 100 1/20 = .05 Slide 10 Using Excel to Construct Relative Frequency and Percent Frequency Distributions s Formula Worksheet C D Frequency =COUNTIF($A$2:$A$21,C2) =COUNTIF($A$2:$A$21,C3) =COUNTIF($A$2:$A$21,C4) =COUNTIF($A$2:$A$21,C5) =COUNTIF($A$2:$A$21,C6) =SUM(D2:D6) E Relative Frequency =D2/$D$7 =D3/$D$7 =D4/$D$7 =D5/$D$7 =D6/$D$7 =SUM(E2:E6) F Percent Frequency =E2*100 =E3*100 =E4*100 =E5*100 =E6*100 =SUM(F2:F6) 1 2 3 4 5 6 7 8 Quality Rating Poor Below Average Average Above Average Excellent Total Note: Columns AB and rows 921 and are not shown. Slide 11 Using Excel to Construct Relative Frequency and Percent Frequency Distributions s Value Worksheet C D Frequency 2 3 5 9 1 20 E Relative Frequency 0.10 0.15 0.25 0.45 0.05 1.00 F Percent Frequency 10 15 25 45 5 100 1 2 3 4 5 6 7 8 Quality Rating Poor Below Average Average Above Average Excellent Total Note: Columns AB and rows 921 and are not shown. Slide 12 Bar Graph A bar graph is a graphical device for depicting qualitative data. On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis). Using a bar of fixed width drawn above each class label, we extend the height appropriately. The bars are separated to emphasize the fact that each class is a separate category. Slide 13 Bar Graph 10 9 8 Frequency 7 6 5 4 3 2 1 Poor Below Average Above Excellent Average Average Rating Slide 14 Marada Inn Quality Ratings Using Excel's Chart Wizard to Construct Bar Graphs Step 1 Select cells C1:D6 Step 2 Click the Chart Wizard button Step 3 When the Chart Type dialog box appears: Choose Column in the Chart type list Choose Clustered Column from the Chart subtype display Click Next > Step 4 When the Chart Source Data dialog box appears Click Next > ... continued Slide 15 Using Excel's Chart Wizard to Construct Bar Graphs Step 5 When the Chart Options dialog box appears: Select the Titles tab and then Type Marada Inn Quality Ratings in the Chart title box Type Quality Rating in the Value (X) axis box Type Frequency in the Value (Y) axis box Select the Legend tab and then Remove the check in the Show Legend box Click Next > ... continued Slide 16 Using Excel's Chart Wizard to Construct Bar Graphs Step 6 When the Chart Location dialog box appears: Specify the location for the new chart Click Finish to display the bar graph Slide 17 Using Excel's Chart Wizard to Construct Bar Graphs C 9 10 11 12 13 14 15 16 17 18 19 20 21 D E Marada Inn Quality Ratings 10 Frequency 8 6 4 2 0 Poor Below Average Average Above Average Excellent Quality Rating Slide 18 Pie Chart The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. s First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. s Since there are 360 degrees in a circle, a class with a relative frequency of .25 would consume .25(360) = 90 degrees of the circle. Slide 19 Pie Chart Marada Inn Quality Ratings Excellent 5% Poor 10% Below Average 15% Above Average 45% Average 25% Slide 20 Example: Marada Inn s Insights Gained from the Preceding Pie Chart Onehalf of the customers surveyed gave Marada a quality rating of "above average" or "excellent" (looking at the left side of the pie). This might please the manager. For each customer who gave an "excellent" rating, there were two customers who gave a "poor" rating (looking at the top of the pie). This should displease the manager. Slide 21 Using Excel's Chart Wizard to Construct Pie Charts Step 1 Select cells C2:C6 and F2:F6 Step 2 Click the Chart Wizard button Step 3 When the Chart Type dialog box appears: Choose Pie in the Chart type list Choose Pie from the Chart subtype display Click Next > Step 4 When the Chart Source Data dialog box appears Click Next > ... continued Slide 22 Using Excel's Chart Wizard to Construct Pie Charts Step 5 When the Chart Options dialog box appears: Select the Titles tab and then Type Marada Inn Quality Ratings in the Chart title box Select the Legend tab and then Remove the check in the Show Legend box Select the Data Labels tab and then Select Show Label and percent Select Show leader lines Click Next > ... continued Slide 23 Using Excel's Chart Wizard to Construct Pie Charts Step 6 When the Chart Location dialog box appears: Specify the location for the new chart Click Finish to display the pie chart Slide 24 Using Excel's Chart Wizard to Construct Pie Charts C 9 10 11 12 13 14 15 16 17 18 19 20 D E Marada Inn Quality Ratings Excellent 5% Poor 10% Below Average 15% Above Average 45% Average 25% Slide 25 Summarizing Quantitative Data s s s s s Frequency Distribution Relative Frequency and Percent Frequency Distributions Histogram Cumulative Distributions Ogive Slide 26 Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tuneups performed in the shop. She examines 50 customer invoices for tuneups. The costs of parts, rounded to the nearest dollar, are listed on the next slide. Slide 27 Example: Hudson Auto Repair s Sample of Parts Cost for 50 Tuneups 91 71 104 85 62 78 69 74 97 82 93 72 62 88 98 57 89 68 68 101 75 66 97 83 79 52 75 105 68 105 99 79 77 71 79 80 75 65 69 69 97 72 80 67 62 62 76 109 74 73 Slide 28 Frequency Distribution s Guidelines for Selecting Number of Classes Use between 5 and 20 classes. Data sets with a larger number of elements usually require a larger number of classes. Smaller data sets usually require fewer classes Slide 29 Frequency Distribution s Guidelines for Selecting Width of Classes Use classes of equal width. Approximate Class Width = Largest Data Value - Smallest Data Value Number of Classes Slide 30 Frequency Distribution For Hudson Auto Repair, if we choose six classes: Approximate Class Width = (109 52)/6 = 9.5 Frequency Parts Cost ($) 5059 2 6069 13 7079 16 8089 7 9099 7 100109 5 Total 50 Slide 31 10 Using Excel's FREQUENCY Function to Construct a Frequency Distribution s Formula Worksheet (showing data entered) A B C Parts Parts Cost Cost 91 50-59 71 60-69 104 70-79 85 80-89 62 90-99 78 100-109 69 Note: Rows 951 are not shown. Slide 32 D Frequency 1 2 3 4 5 6 7 8 Using Excel's FREQUENCY Function to Construct a Frequency Distribution s s s s The FREQUENCY function is not a "simple" Excel function. FREQUENCY is capable of providing multiple values. In Excel, a formula that can return multiple values is called an array formula. An array formula must be entered in a special way. Slide 33 Using Excel's FREQUENCY Function to Construct a Frequency Distribution s Entering the Necessary Array Formula Step 1 Select D2:D7 (where the frequencies will appear) Step 2 Type the following formula: =FREQUENCY(A2:A51,{59,69,79,89,99,109}) Step 3 Press CTRL + SHIFT + ENTER (Array formula will be entered in D2:D7) Slide 34 Using Excel's FREQUENCY Function to Construct a Frequency Distribution s Formula Worksheet A B C Parts Parts Cost Cost 91 50-59 71 60-69 104 70-79 85 80-89 62 90-99 78 100-109 69 D Frequency =FREQUENCY(A2:A51,{59,69,79,89,99,109}) =FREQUENCY(A2:A51,{59,69,79,89,99,109}) =FREQUENCY(A2:A51,{59,69,79,89,99,109}) =FREQUENCY(A2:A51,{59,69,79,89,99,109}) =FREQUENCY(A2:A51,{59,69,79,89,99,109}) =FREQUENCY(A2:A51,{59,69,79,89,99,109}) 1 2 3 4 5 6 7 8 Note: Rows 951 are not shown. Slide 35 Using Excel's FREQUENCY Function to Construct a Frequency Distribution s Value Worksheet A B C Parts Parts Cost Cost 91 50-59 71 60-69 104 70-79 85 80-89 62 90-99 78 100-109 69 Note: Rows 951 are not shown. Slide 36 D Frequency 2 13 16 7 7 5 1 2 3 4 5 6 7 8 Relative Frequency and Percent Frequency Distributions Parts Relative Percent Cost ($) Frequency Frequency 5059 .04 4 6069 .26 2/50 26 .04(100) 7079 .32 32 8089 .14 14 9099 .14 14 100109 .10 10 Total 1.00 100 Slide 37 Example: Hudson Auto Repair s Insights Gained from the Percent Frequency Distribution Only 4% of the parts costs are in the $5059 class. 30% of the parts costs are under $70. The greatest percentage (32% or almost onethird) of the parts costs are in the $7079 class. 10% of the parts costs are $100 or more. Slide 38 Histogram Another common graphical presentation of quantitative data is a histogram. The variable of interest is placed on the horizontal axis. A rectangle is drawn above each class interval with its height corresponding to the interval's frequency, relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes. Slide 39 Histogram Tuneup Parts Cost 18 16 14 Frequency 12 10 8 6 4 2 Parts 50 60 70 80 90 100 110 120 Cost ($) Slide 40 Using Excel's Chart Wizard to Construct a Histogram Step 1 Select cells C1:D7 Step 2 Click the Chart Wizard button Step 3 When the Chart Type dialog box appears: Choose Column in the Chart type list Choose Clustered Column from the Chart subtype display Click Next > Step 4 When the Chart Source Data dialog box appears Click Next > ... continued Slide 41 Using Excel's Chart Wizard to Construct a Histogram Step 5 When the Chart Options dialog box appears: Select the Titles tab and then Type Tuneup Parts Cost in the Chart title box Type Parts Cost ($) in the Value (X) axis box Type Frequency in the Value (Y) axis box Select the Legend tab and then Remove the check in the Show Legend box Click Next > ... continued Slide 42 Using Excel's Chart Wizard to Construct a Histogram Step 6 When the Chart Location dialog box appears: Specify the location for the new chart Click Finish to display the histogram Slide 43 Using Excel's Chart Wizard to Construct a Histogram C 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 D E Tune-up Parts Cost 20 Frequency 15 10 5 0 50-59 60-69 70-79 80-89 90-99 100-109 Parts Cost ($) Slide 44 Using Excel's Chart Wizard to Construct a Histogram s Eliminating Gaps Between Rectangles Step 1 Right click on any rectangle in the column chart Step 2 Choose the Format Data Series option Step 3 When the Format Data Series Option dialog box appears Select the Options tab and then Enter 0 in the Gap width box Click OK Slide 45 Using Excel's Chart Wizard to Construct a Histogram C 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 D E Tune-up Parts Cost 20 Frequency 15 10 5 0 50-59 60-69 70-79 80-89 90-99 100-109 Parts Cost ($) Slide 46 Cumulative Distributions Cumulative frequency distribution - shows the number of items with values less than or equal to the upper limit of each class.. Cumulative relative frequency distribution shows the proportion of items with values less than or equal to the upper limit of each class. Cumulative percent frequency distribution shows the percentage of items with values less than or equal to the upper limit of each class. Slide 47 Cumulative Distributions s Hudson Auto Repair Cumulative Cumulative Cumulative Relative Percent Frequency Frequency Cost ($) Frequency 2 .04 < 59 4 15 .30 < 69 30 < 79 31 2 + 13 .62 15/50 62 .30(100) 38 .76 < 89 76 45 .90 < 99 90 1.00 < 109 50 100 Slide 48 End of Chapter 2, Part A Slide 49 ...
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