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Unit 2 Displaying Data (Chapt. 3: The Histogram) Graphical displays for analysis & presentation Unit 2 Displaying Data (Chapt. 3: The Histogram) Graphical displays for analysis & presentation of data. The Current Population Survey collects data on many variables. A VARIABLE is a characteristic which may differ from person to 2 -1 person in a study. Display A. 05

Some Survey Questions Question asked in a survey type. Corresponding. Variable. • How old Some Survey Questions Question asked in a survey type. Corresponding. Variable. • How old are you? • How many people in your family? • Are you currently married? • How many rooms in your house? • How tall are you? • What is your major? • Where were you born? 2 -2 Display • How much do you like chocolate? very much / somewhat / so-so / not much / not at all

Variable types Variables and data can be: qualitative - the answer to the question Variable types Variables and data can be: qualitative - the answer to the question is not a number quantitative - the answer to the question is a number qualitative data can be: - discrete - takes on particular values only - continuous - can be measured in arbitrarily small amounts Another classification system: nominal - categorical ordinal - values fall in ordered 2 -3 categories, may be numerical Display interval - can be ordered AND we can indicate an exact distance between values

Qualitative includes ____ and ____ data types. Quantitative includes ____ and ____ data types. Qualitative includes ____ and ____ data types. Quantitative includes ____ and ____ data types. 2 -4 Display

Pie chart & Bar chart CORPORATION MARKET SHARE (%) Coca-Cola Co. Pepsico Inc. 27. Pie chart & Bar chart CORPORATION MARKET SHARE (%) Coca-Cola Co. Pepsico Inc. 27. 4 Dr Pepper Co. Seven-Up Co. RJR Nabisco 4. 6 Royal Crown Cola Co. Others 12. 5 38. 6 7. 1 6. 3 3. 5 2 -5 Display

Bar Chart for Cola Data 2 -6 Display Bar Chart for Cola Data 2 -6 Display

Soft Drinks Revisited N a DP Pe Co Oth 7 U RC 2 -7 Soft Drinks Revisited N a DP Pe Co Oth 7 U RC 2 -7 Display

2 -8 Display 2 -8 Display

The Pareto Diagram The (frequency) Pareto Diagram is a bar chart which displays the The Pareto Diagram The (frequency) Pareto Diagram is a bar chart which displays the causes of various defects, in order, from most to least frequent so that you can focus attention on the most important problems. 2 -9 Display

National Demonstration Project • Park Nicollet Pareto diagram with listing of Possible Causes for National Demonstration Project • Park Nicollet Pareto diagram with listing of Possible Causes for Patient Dissatisfaction 2 -10 Display

Hot Dogs ( Consumer Reports ) 2 -11 Display Hot Dogs ( Consumer Reports ) 2 -11 Display

Steps in Constructing A Stem-and-Leaf Diagram (1) Scan the data for approximate range. Choose Steps in Constructing A Stem-and-Leaf Diagram (1) Scan the data for approximate range. Choose a suitable pair of adjacent digits (eg. tens and ones). (2) Allocate a separate line in the display for each possible string of leading digits (STEM). (3) Split each data value between the selected two digits. (4) Write down the trailing digit(s) (LEAF) for each data value on the line corresponding to its leading digits. Sort the leaves. Provide a relevant key. 2 -12 Display

Stem - & -Leaf diagram Data from 25 subjects in a survey case # Stem - & -Leaf diagram Data from 25 subjects in a survey case # age sex marital status # children husb. educ. level ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 70 M 28 F 47 M 48 M college grad 23 M h. s. grad 69 F grade 31 F Master's degree 70 F 80 F grade 37 F 65 F 71 F 41 F 70 M grade 56 F grad 8 th grade 34 F grade 48 F 43 F 50 F 24 F college grad 23 M college grad wife --------- married separated married 3 3 1 3 h. s. grad college grad h. s. grad college grad married 0 college grad divorced 3 -- married some grad work 1 grad 8 th single 0 widowed 0 --- h. s. grad less than 8 th married single widowed married 3 0 2 3 5 h. s. grad --h. s. grad some h. s. grad less than 8 th married 1 married 4 grad 8 th grade 2 -13 some h. s. grad 8 th Display married divorced married 6 3 1 2 h. s. grad some h. s. -college grad h. s. grad some h. s. college grad married 1 college grad

2 -14 Display 2 -14 Display

Stem-&-Leaf of Ages STEM AND LEAF PLOT OF AGE, MINIMUM IS: 21. 0 LOWER Stem-&-Leaf of Ages STEM AND LEAF PLOT OF AGE, MINIMUM IS: 21. 0 LOWER HINGE IS: MEDIAN IS: 47. 0 UPPER HINGE IS: MAXIMUM IS: 80. 0 3 H 4 M 5 6 H 7 8 N = 25 31. 0 65. 0 2 13348 1147 137788 06 359 0001 0 2 -15 Display

Age Data - Histogram (FPP) In a histogram, the areas of the blocks represent Age Data - Histogram (FPP) In a histogram, the areas of the blocks represent percentages. In a histogram, the area of each block represents the percentage of observations in the corresponding interval. 7 6 5 4 0. 25 0. 20 0. 15 3 2 1 0. 10 0. 05 20 50 80 110 AGE 7 6 5 4 0. 25 0. 20 0. 15 3 2 1 0. 10 0. 05 20 50 80 AGE 110 2 -16 Display

What to Look for in a Histogram 1. Look at the shape. Is it What to Look for in a Histogram 1. Look at the shape. Is it symmetric? skewed? 2. Detect outliers, if any. 3. Where is the average? 2 -17 Display

Basic Shapes of Histograms Normal, Triangular, Symmetric Skewed to left Bimodal Uniform, Rectangular Skewed Basic Shapes of Histograms Normal, Triangular, Symmetric Skewed to left Bimodal Uniform, Rectangular Skewed to right J-shaped 2 -18 Display

Back-to-Back Displays Weights of 50 college students (in pounds) Student 1 2 7 8 Back-to-Back Displays Weights of 50 college students (in pounds) Student 1 2 7 8 Male/Female F F F M Weight 98 150 118 167 3 9 M M 108 170 4 10 F F 158 120 5 6 M M 162 112 Student 11 17 Male/Female M Weight 177 137 12 18 M F 186 205 13 19 M M 191 190 14 20 M M 128 120 15 16 F F 135 F Student 21 27 Male/Female F Weight 188 162 22 28 M M 176 157 23 29 M M 118 154 24 30 F M 168 148 25 26 M M 115 F Student 31 37 Male/Female F Weight 101 154 32 38 F M 143 116 33 39 M F 145 161 34 40 M M 108 165 35 36 F M 155 M Display Student 41 47 Male/Female 42 48 F 43 49 M 44 50 F 45 46 M M 195 115 2 -19 110

Back-to-Back Displays - 2 09 10 11 12 13 14 15 16 17 18 Back-to-Back Displays - 2 09 10 11 12 13 14 15 16 17 18 19 20 21 Stem-&-Leaf 8 Diagram 188 0255688 00089 257 2358 044578 122578 FEMALE 00667 3468 8 09 0155 881 10 5 8865520 11 5 98000 12 752 13 14 2 3 5 8 15 0 4 4 5 7 8 16 Back-to-Back 1 2 2 5 7 8 17 Stem-&-Leaf 0 0 6 6 7 Diagram 18 3 4 6 8 19 0 1 5 5 20 5 21 5 2 -20 Display

Back-to-Back Displays - 3 2 -21 Display Back-to-Back Displays - 3 2 -21 Display

Time Series Plots Time in seconds 160 140 120 100 80 60 40 20 Time Series Plots Time in seconds 160 140 120 100 80 60 40 20 Day 5 10 15 20 25 30 35 40 45 50 55 Average Time for Receptionist to Answer Telephones Between 9: 00 and 10: 00 a. m. (Park Nicollet Project) 2 -22 Display

Control Charts 2 -23 Display Control Charts 2 -23 Display

Newspaper Graphics Examples 2 -24 Display Newspaper Graphics Examples 2 -24 Display

2 -25 Display 2 -25 Display

2 -26 Display 2 -26 Display

The Pareto Diagram The (frequency) Pareto Diagram is a bar chart which displays the The Pareto Diagram The (frequency) Pareto Diagram is a bar chart which displays the causes of various defects, in order, from most to least frequent so that you can focus attention on the most important problems. 2 -27 Display

Pareto Diagram Wooden glass doors are produced on a six day work week. At Pareto Diagram Wooden glass doors are produced on a six day work week. At final checkout before shipping, the doors are inspected and each is classified as conforming or nonconforming. Nonconforming doors are further classified into one of the following categories, according to their defect. The data here give the number of defective doors by day and by classification. A Pareto chart can be made to show which type of defect is most prevalent. Day: Day inspected Window: Window misaligned Discolor: Discolor Handle: Handle hole missing Hinges: Hinges wrong Rough: Rough wood Glass: Broken glass Warped: Warped 2 -28 Display Variables are: Day Window Discolor Handle Hinges Rough Glass Warped

Day Window Discolor Handle Hinges 1 4 2 3 3 1 4 1 5 Day Window Discolor Handle Hinges 1 4 2 3 3 1 4 1 5 6 1 8 9 10 11 12 13 15 16 17 18 19 20 22 23 24 1 25 2 26 27 1 29 30 1 3 Rough 2 Glass Warped 1 2 2 7 3 2 2 3 1 4 4 3 1 1 1 Pareto Charts Total 31 6 1 2 2 4 1 1 1 2 1 5 1 4 4 1 1 2 2 2 1 6 3 2 1 1 3 2 2 1 2 2 3 4 3 2 1 2 -29 Display 1 2 24 24 47 5 24 12 14

Frequency Pareto Chart 50 40 Count 30 20 10 Hinge Color Wood Hole Warp Frequency Pareto Chart 50 40 Count 30 20 10 Hinge Color Wood Hole Warp Glass Window Problem 2 -30 Display

Pareto Charts - 2 A Pareto Diagram can be made to display the costs Pareto Charts - 2 A Pareto Diagram can be made to display the costs of various defects, in order, so that you can focus attention on the most important problems. The following costs can be assumed for each of the defect types. Day: Day Inspected Window: Window misaligned $10. 00 • Discolor: Discolor 5. 00 Handle: Handle hole missing 3. 00 Hinges: Hinges wrong 6. 00 Rough: Rough wood 5. 00 Glass: Broken glass 8. 00 Warped: Warped 45. 00 2 -31 Display

Cost Pareto Chart 600 500 400 cost ($) 300 200 100 Warp Hinge Color Cost Pareto Chart 600 500 400 cost ($) 300 200 100 Warp Hinge Color Wood Glass Hole Window Problem 2 -32 Display