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Data Visualisation
This document discusses various tools and methods for data visualization. It describes: 1) The key purposes of data visualization as conveying information through visual representations to give viewers insight into data structures and relationships. 2) Common diagrammatic representations like bar diagrams, pie charts, and pictograms as well as graphic representations like histograms and frequency curves. 3) How to construct different types of bar diagrams, pie charts, and pictograms to visually display one or more variables and their relationships in data. 4) The use of deviation bars to represent net excess or deficits and percentage bar diagrams to show components as a percentage of the total.
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Data Visualisation
- 1. Data Visualization Dr. AmitabhMishra 1 24% 18% 13% 18% 11% 7% 9%
- 2. Data Visualization orPresentation • Data visualization means- “to convey information through visual representations” • Visalisation tools produces “interactive visual representations of data to reinforce human cognition; enabling the viewer to gain knowledge about the internal structure of the data and causal relationships in it” Dr. Amitabh Mishra 2
- 3. Significance of Visualization/ Presentation •They give a bird’s eye view of entire data • They are attractive to the eye • They have great memorizing effect • They facilitate comparison • They give visual indications of – Magnitudes, – Grouping, – Trends and patterns Dr. Amitabh Mishra 3
- 4. Functions of Visualization/ Presentation •Three functions of visualization are: – Record i.e. Store information – Analyze i.e. Support reasoning about information – Communicate i.e. Convey information to others Dr. Amitabh Mishra 4
- 5. Tools for Visualization (Diagrammatic& Graphic Representation) Visualization/ Representation Diagrammatic Representation Bar-diagram Pie-chart Pictogram Graphic Representation Histogram Frequency Polygon Smoothed Frequency Curve Cumulative Frequency Curve (Ogive) Dr. Amitabh Mishra 5
- 6. Tools for Visualization (Diagrammatic& Graphic Representation) • Diagrammatic Representation a) Bar-diagram (One dimensional diagram) b) Pie-chart (Two dimensional diagram) c) Pictogram/ Cartograms (Statistical Maps) • Graphic Representation a) Histogram b) Frequency Polygon c) Smoothed Frequency Curve d) Cumulative Frequency Curve (Ogive) Dr. Amitabh Mishra 6
- 7. DIAGRAMMATIC REPRESENTATION Dr. AmitabhMishra 7 -20% 0% 20% 40% 60% 80% 100% 1986 1987 1988 profit/loss polishing other cost wages
- 8. Types of Diagram Dr.Amitabh Mishra 8 Diagrammatic Representation Bar-diagram (One Dimensional Diagram) Pie-chart (Two Dimensional Diagram Pictogram/Cartograms (Statistical Maps)
- 9. BAR DIAGRAM One DimensionalDiagram Dr. Amitabh Mishra 9 0 100 200 300 400 500 600 700 1993-94 1994-95 1995-95 Rs lakhs years
- 10. Bar Diagram • “Bar-Diagramare vertical lines where length of the bars are proportional to their corresponding numerical values”. • “Bar is a thick line whose width is shown merely for attention”. – But, all bars should have the same width so as not to confuse the reader of diagram. • It is called one dimensional diagram because it is only length of bar which matters not the width. Dr. Amitabh Mishra 10
- 11. • Width ofbars should be uniform through out the diagram • The gap between one diagram and other should be uniform • Bars may be either – Horizontal or – Vertical • The vertical bars should be preferred because they give a better look Dr. Amitabh Mishra 11 C4 1Q 4Q 3Q 2Q 1Q 1.5 1.2 0.9 0.6 0.3 0.0 Figure 1-11:SHIFTINGGEARS 2003 2004 Quartely netincome for General Motors (inbillions)
- 12. Types of BarDiagram Dr. Amitabh Mishra 12 Bar Diagram Simple bar diagram Sub-divided Bar diagram Multiple-bars diagram Percentage-bar diagram Deviation bars diagram
- 13. Types of BarDiagram 1. Simple bar diagram 2. Sub-divided Bar diagram 3. Multiple-bars diagram 4. Percentage-bar diagram 5. Deviation bars. Dr. Amitabh Mishra 13
- 14. Simple Bar diagram •It is used to represent only one variable • Ex- – Figures of sales for various years – Figures of production for various years – Figures of population for various years Dr. Amitabh Mishra 14
- 15. • Following tablegives birth rate per thousand of different countries over a period of time. Dr. Amitabh Mishra 15 0 5 10 15 20 25 30 35 40 45 india germany united kingdom china new zeland swedan birth rate per thousand of different countries Country Birth rate India 33 Germany 16 U.K 20 China 40 Newzealand 30 Swedan 15
- 16. Example 2: Fund flowfor various years may be shown by means of a simple bar-diagram Year Funds Flow (Rs. crores) 2009-10 85.80 2010-11 109.61 2011-22 204.29 2012-13 126.31 Dr. Amitabh Mishra 16 0 50 100 150 200 250 2009-10 2010-11 2011-12 2012-13 Funds Flow Funds Flow
- 17. Exercise: 1 Prepare aSimple bar diagram for your internal and external marks in previous semester examination Subject Name External Marks Internal Marks Total Marks Marketing 67 30 97 Organizational Behavior 55 25 80 Accounting 45 20 65 Computer Application 60 28 88 Statistics 39 21 60 Production & Operations 48 25 73 Dr. Amitabh Mishra 17 0 10 20 30 40 50 60 70 80 Marketing Organizational Accounting Computer Application Statistics Production & Operations Marketing Organizati onal Accounting Computer Application Statistics Production & Operations External Marks 67 55 45 60 39 48 External Marks
- 18. Sub-divided Bar Diagram •“In Sub divided Bar Diagram each bar representing the magnitude of given phenomenon is further subdivided in its various components”. • Each component occupies a part of the bar proportional to its share in total. Dr. Amitabh Mishra 18
- 19. • The growthof production of fish for the period 1950-51 to 1986-87 is- (In lakh tonnes). Dr. Amitabh Mishra 19 0 5 10 15 20 25 30 35 1950-51 1960-61 1970-71 1980-81 1984-85 1985-86 PRODUCTION OF FISH YEARS inland marine Year Marine Inland total 1950-51 5.34 2.18 7.52 1960-61 8.80 2.80 11.60 1970-71 10.86 6.70 17.56 1980-81 15.55 8.87 24.42 1984-85 16.98 11.03 28.01 1985-86 17.16 11.60 28.76 1986-87 12.47 8.42 20.89
- 20. Exercise Prepare a sub-dividedbar diagram for your internal and external marks in previous semester examination Subject Name External Marks Internal Marks Total Marks Marketing 67 30 97 Organizational Behavior 55 25 80 Accounting 45 20 65 Computer Application 60 28 88 Statistics 39 21 60 Production & Operations 48 25 73 Dr. Amitabh Mishra 20 Marketi ng Org Beha Accoun ting Comp App Statistic s Pro & Oper Internal 30 25 20 28 21 25 External 67 55 45 60 39 48 0 20 40 60 80 100 120 MArks internal and external marks
- 21. Multiple-bars diagram • Inmultiple bars “two or more set of interrelated data are represented”. • This diagram should be preferred, when ever comparison between two or more related variables is to be made. Dr. Amitabh Mishra 21
- 22. 0 20 40 60 80 100 120 140 160 1984 1985 19861987 sales gross profit net profit Dr. Amitabh Mishra 22 • Draw a suitable diagram from the following data- Year Sales Gross profit Net profit 1984 120 40 20 1985 135 45 20 1986 140 55 35 1987 150 60 40
- 23. 2002-03 2003-04 Gross profits Profitsbefore tax Profit after tax Retained profits 3104 1663 1219 846 3123 1376 982 589 Dr. Amitabh Mishra 23 3104 3123 1663 1376 1219 982 846 589 0 500 1000 1500 2000 2500 3000 3500 2002-03 2003-04 Gross Profits Profits Before Tax Profit After Tax Retained Profits
- 24. Percentage-bar diagram • “Sub-dividedbar chart drawn on percentage basis is known as percentage bar diagram”. • In Percentage bar diagram, we express each component as the percentage of its respective total. • Bars of length equal to 100 for each class are drawn at first step and sub-divided in the proportion of the percentage of their component in the second step. Dr. Amitabh Mishra 24
- 25. • Represent thefollowing by sub divided bar diagram on percentage basis- Dr. Amitabh Mishra 25 Particulars 1986 1987 1988 Cost/chair Wages 9 15 21 Other costs 6 10 14 Polishing 3 5 7 Total 18 30 42 Proceeds /chair 20 30 40 Profit/loss +2 - -2
- 26. Particulars 1986 19871988 Cost/chair Wages 45 50 52.5 Other costs 30 33.3 35 Polishing 15 16.7 17.5 Total cost 90 100 105 Sales price 100 100 100 Profit/loss +10 - -5.0 -20% 0% 20% 40% 60% 80% 100% 1986 1987 1988 profit/loss polishing other cost wages Dr. Amitabh Mishra 26 Take the sales price/chair as 100 and express the other figures in percentages. The percentages so obtained are given below-
- 27. Items Expenses % Expense s Food Clothing House Rent Education 5550 5100 4800 4950 27.21% 25% 23.53% 24.26% Total20400 100% Dr. Amitabh Mishra 27 27.21 25 24.26 23.53 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% %Expenses education house rent clothing food
- 28. Deviation Bar-diagram • Deviationbars are popularly used for representing net quantity- excess or deficit i.e. – Net profit, – Net loss, – Net exports, or – Net imports, etc. • Such bars can have both positive and negative values. Positive values are shown above the base line and negative values below it. Dr. Amitabh Mishra 28
- 29. Year Sales Net profits 2011-12 14% 29% 2012-13 11%61% 2013-14 17% -21% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70% sales net profit 2001-02 2002-03 2003-04 Dr. Amitabh Mishra 29 2001-02 2002-03 2003-04 sales 14% 11% 17% net profit 29% 61% -21%
- 30. Two dimensional diagram or SurfaceDiagram/ Area Diagram 1. Pie diagrams. Dr. Amitabh Mishra 30
- 31. Pie Charts or Round 1st Qtr 2ndQtr 3rd Qtr 4th Qtr Dr. Amitabh Mishra 31
- 32. • “A piechart is a circular chart in which the circle is divided into sectors. Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set”. • Pie charts are useful to compare different parts of a whole amount. Dr. Amitabh Mishra 32
- 33. • A piechart is not useful for displaying relationships over time or relationships among several variables. • A pie chart should not require more than seven sections. • The steps to draw a pie diagram are: – Convert the various observations (in percent) in the data set into corresponding degree in the circle by multiplying each by 3.6 (360 /100) – Draw the circle and its parts using different degrees 33 Dr. Amitabh Mishra
- 34. Example • Draw apie chart for the following data of 6th five year plan public sector outlays: Dr. Amitabh Mishra 34 Sector Percentage outlay Agricultural and rural development 12.9% Irrigation etc. 12.5% Energy 27.2% Industry and mineral 15.4% Transport, communication etc. 15.9% Social service and other 16.1%
- 35. The angle atthe centre is given by- =(Percentage outlay/100)x 360 = Percentage outlay x 3.6 Dr. Amitabh Mishra 35 Sector Percentage outlay Angle at the centre Agricultural and rural development 12.9% 12.9 x 3.6 = 46° Irrigation etc. 12.5% 12.5 x 3.6 = 45° Energy 27.2% 27.2 x 3.6 =98° Industry and mineral 15.4% 15.4 x 3.6 = 56° Transport, communication etc. 15.9% 15.9 x 3.6 = 57° Social service and other 16.1% 16.1 x 3.6 = 58° Total 100% 360°
- 36. Dr. Amitabh Mishra36 13% 13% 15% 16% 16% 27% Percentage outlay Agricultural and rural development Industry and mineral Transport, communication etc. Social service and other Energy
- 37. U.S. Auto Sales2003 - 2007 37 Dr. Amitabh Mishra
- 38. Pie Chart of2007 U.S. Auto Sales 24% 18% 13% 18% 11% 7% 9% GM Ford Chrysler Toyota Honda Nissan Other 38 Dr. Amitabh Mishra
- 39. 46% 27% 19% 5% 3% Column2 Pacific Atlantic Indian Antarctic arctic Dr. AmitabhMishra 39 Ocean Area % Area Degree Pacific Atlantic Indian Antarctic arctic 70.8 41.2 28.5 7.6 4.8 46.31 26.94 18.64 4.96 3.15 166.70 97.00 67.10 17.89 11.31 Total 152.9 100.00 360.00
- 40. Pictographs • “A pictographuses small pictures or symbols to display the data”. • Pictographs do not depict results precisely. Hence, caution should be exercised when using them. • To construct pictograms the following suggestions are made: – The symbols must be simple and clear. – The quantity represented by a symbol should be given. 40 Dr. Amitabh Mishra
- 41. Pictograph for 2007U.S. Auto Sales *Each Symbol Equals 1,000,000 Units GM Chrysler Toyota Honda Nissan Other Ford 41 Dr. Amitabh Mishra
- 42. Dr. Amitabh Mishra42 Example of pictogram: Year Output 1999 2000 2001 2002 2004 2996 4052 5924 Output of cars during the year by a car manufacturing company: 1999 2000 2001 2002 Scale = 1000 cars
- 43. Types of Graphs graphs Graphsof time series or Line graphs Graph of frequency distribution Dr. Amitabh Mishra 43
- 44. Line graphs or graph oftime series • Graph of one variable. • Graph of two or more variables. • Graph having two scales. • Range chart • Band graph. • Ratio chart. Dr. Amitabh Mishra 44
- 45. Graph of frequencydistribution • Histogram • Frequency Polygon. • Smoothed frequency curve. • Ogives or cumulative frequency curves. Dr. Amitabh Mishra 45
- 46. A histogramis a chart made of bars of different heights. Widths and locations of bars correspond to widths and locations of data groupings Heights of bars correspond to frequencies or relative frequencies of data groupings Histogram 46 Dr. Amitabh Mishra
- 47. Frequency Histogram Histogram Example 47 Dr.Amitabh Mishra
- 48. Relative Frequency Histogram HistogramExample 48 Dr. Amitabh Mishra
- 49. Figure 23.6 Histogram of2007 U.S. Auto Sales 0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 GM Ford Chrysler Toyota Honda Nissan other 49 Dr. Amitabh Mishra
- 50. Pie Charts Categoriesrepresented as percentages of total Bar Graphs Heights of rectangles represent group frequencies Frequency Polygons Height of line represents frequency Ogives Height of line represents cumulative frequency Time Plots Represents values over time 1-8 Methods of Displaying Data 50 Dr. Amitabh Mishra
- 51. Pie Chart 33.0% 23.0% 19.0% 19.0% 6.0% Category Happy withcareer Don't like my job but it is on my career path Job is OK, but it is not on my career path Enjoy job, but it is not on my career path My job just pays the bills Figure 1-10: Twentysomethings split on job satisfication My job just pays the bills Happy with career Enjoy job, but it is not on my career path Job OK, but it is not on my career path Do not like my job, but it is on my career path 51 Dr. Amitabh Mishra
- 52. Relative Frequency PolygonOgive Frequency Polygon and Ogive 50 40 30 20 10 0 0.3 0.2 0.1 0.0 Sales 50 40 30 20 10 0 1.0 0.5 0.0 Sales (Cumulative frequency or relative frequency graph) 52 Dr. Amitabh Mishra
- 53. O S A J J M A M F J D N O S A J J M A M F J D N O S A J J M A M F J 8.5 7.5 6.5 5.5 Month M i l l i o n s o f T o n s Mo nthly Ste e l P ro d uc tio n Time Plot 53 Dr. Amitabh Mishra
- 54. Scatter Plots • ScatterPlots are used to identify and report any underlying relationships among pairs of data sets. • The plot consists of a scatter of points, each point representing an observation. 54 Dr. Amitabh Mishra
- 55. Scatter Plots • Scatterplot with trend line. • This type of relationship is known as a positive correlation. Correlation will be discussed in later chapters. 55 Dr. Amitabh Mishra
- 56. U.S. Auto Sales2003 - 2007 56 Dr. Amitabh Mishra
- 57. Guidelines for Graphs:Line Charts • A line chart connects a series of data points using continuous lines. • This is an attractive way of illustrating trends and changes over time. • Several series can be compared on the same chart, and forecasts, interpolations, and extrapolations can be shown. 57 Dr. Amitabh Mishra
- 58. Line Chart ofTotal U.S. Auto Sales Fig. 23.3 0 500000 1000000 1500000 2000000 2500000 3000000 3500000 4000000 4500000 5000000 2003 2004 2005 2006 2007 Unit Sales Year GM Ford Chrysler Toyota Honda Nissan Other 58 Dr. Amitabh Mishra
- 59. Guidelines for Graphs:Line Charts • A stratum chart is a set of line charts in which the data are successively aggregated over the series. • Areas between the line charts display the magnitudes of the relevant variables. 59 Dr. Amitabh Mishra
- 60. Fig. 23.4 Stratum Chartof Total U.S. Auto Sales 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 18000000 20000000 2003 2004 2005 2006 2007 Unit Sales Year Other Nissan Honda Toyota Chrysler Ford GM 60 Dr. Amitabh Mishra
- 61. Guidelines for Graphs: Histogramsand Bar Charts • A bar chart displays data in various bars that may be positioned horizontally or vertically. • The histogram is a vertical bar chart in which the height of the bars represents the relative or cumulative frequency of occurrence of a specific variable. 61 Dr. Amitabh Mishra