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Lecture Series on Statistics No. Biostat_4 Date – 10.08.2008 Understanding Data through Presentation Dr. Bijaya Bhusan Nanda, M. Sc (Gold Medalist) Ph. D. (Stat.) Topper Orissa Statistics & Economics Services, 1988 bijayabnanda@yahoo.com 1
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CONTENT Significance of diagram and graphs Comparison of tabular and diagrammatic, graphics presentation Difference between diagrams and graphs General rule for constructing diagrams and graphs Types of diagrams • Diagrams and graphs for understanding data 2
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Learning Objective Trainee will be able to describe: • significance of diagrams and graphs, Compare between tabular and diagrammatic, graphics presentation; • general rule for constructing diagrams and graphs; • able to construct different types of diagrams and graphs Trainee will be able to use appropriate diagrams and graphs to understand data 3
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Significance of diagram and graphs Gives birds eye view of the entire data. The mind through the eye can more readily appreciate the significance of the figures. Figures are dry but diagram and graphs delight the eye. More popular in exhibition, fairs, conference, board meetings and public functions. Great memorizing effect. Easy and quick comparison. Bring out hidden fact and relationship Stimulate and aid analytical thinking and investigation. 4
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Comparison of tabular, diagrammatic & graphics presentationi. Table contains precise figures, diagrams give only an approximate idea.ii. More information on a number of characteristic can be presented in a table than in one graph or diagrams.iii. Tables require much closer reading and more difficult to interpret than diagrams.iv. Graphs and diagrams have a visual appeal and therefore more impressive to lay man.v. For higher statistical analysis data has to be presented in tabular form 5
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Difference between diagrams and graphs Graphs Diagrams For construction a graph Constructed in paper is required. plain papers. It depicts functional or mathematical relationship More attractive between two variables, whereas diagram does not. to the eye than the graph and as For presenting frequency such are better distribution and time series suited for data, graphs are more publicity and appropriate than diagrams propaganda. 6
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General rule for constructing diagrams and graphs Number Title Proportion between width and height Selection of scale • example “million of tones” number of persons in thousand”, etc. Footnotes Index Neatness and Cleanness Simplicity:- • reader can understand their meaning clearly and easily 7
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Types of diagrams One-dimensional diagram bar diagrams Two dimensional diagram rectangles, squares and circles. Three dimensional diagram cubes, cylinders, and spheres Pictographs and Cartograms 8
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One-dimensional diagram: bar diagrams Only one dimension i.e. length of the bar represents the value of the variable. These are very simple and easy to understand. Bar should be uniform thickness and space between bars should be uniform. The vertical bars may be preferred to horizontal bars and respective figures may be written at the top of the bar. 9
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Types of bar diagrams Simple Bar Diagram: Used to present only one variable for different time period or for different regions Multiple bar diagram: Used to represent two or more sets of inter related data Deviation bar: Used for representing net quantities excess or deficit. Percentage bar: Used to present relative changes in data Sub-divided bar: Each bar is further sub- divided in to various components 10
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Types of bar diagrams Table 3.1 Sex Ratio (females per 000’ males) of Orissa by Social GroupsYear Scheduled Scheduled General Castes Tribes R U T R U T R U T1961 1020 930 1015 1018 946 1016 1013 779 9911971 996 955 993 1009 958 1007 1000 821 9791981 992 951 988 1015 947 1012 994 837 9691991 981 932 975 1006 930 1002 983 849 9592001 983 949 979 1006 948 1003 980 881 960 Source: Census of India, 1961 – 2001 R = Rural, U = Urban, T = Total Please find out the significant features of DATA from the table 11
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Simple Bar Diagram Fig. 3.1 Sex ratio (Females per000 Males) in Orissa: 1961 - 2001 1000 980Sex Ratio 960 940 1961 1971 1981 1991 2001 Year 12
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Multiple Bar DiagramSex ratio (Females per 000 Males) in Orissa by Social Groups 1020 1000Sex Ratio 980 960 940 920 1961 1971 1981 1991 2001 STs SCsCensus Year General Linear (SCs) Linear (STs) Linear (General) 13
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Multiple Bar DiagramRural-Urban difference in the sex ratio in Orissa 250 200 Sex Ratio diff. 150 100 50 0 1961 1971 1981 1991 2001 General Census Year STs SCs Linear (General) Linear (STs) Linear (SCs) 14
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Population of Four Indian States by Broad Age Group: Census 2001 Population in 000’ numbersStates Chhattisg Madhya Age Jharkhand Orissa arh PradeshGroup 0-14 10709 12208 7693 2325215-59 14625 21496 11609 32655 60+ 1579 3039 1504 4281 15
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Sub-divided Bar DiagramFig. 3.4 Distribution of population by age group: Census 2001 60000 50000 0-14 15-59 60+ 40000 30000 20000 10000 0 Jharkhand Orissa Chhattisgarh Madhya Pradesh 16
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Percentage Bar DiagramFig. 3.5 Percentage distribution of population by age group: Census 2001 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Jharkhand Orissa Chhattisgarh Madhya Pradesh 0-14 15-59 60+ 17
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Deviation Bar DiagramRural – Urban Difference in Prevalence of Disability- Census 2001 Prevalence per lakh population 699 700 RUDDP 600 500 442 408 400 305 300 200 100 0 Bargarh Baudh Bhadrak Cuttack Debagarh Dhenkanal -100 -36 -65 18 Year
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Two Dimensional DiagramArea or surface diagram where twodimensions-length and breadth are takeninto consideration to represent the dataseries.Here area of the diagram represents thegiven data.Important types of such diagram are: i) Rectangle, ii) Squares, iii) Circles, iv) Pie diagram 19
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Two Dimensional Diagrami) Rectangle, Since the area of a rectangle is equal to the product of its length and width, while constructing such a diagram both length and width are considered.ii) Squares When the values of the items vary widely, squares should be preferred to rectangles to represent the data. One has to take the square root of the values of the item and then select a suitable scale to draw squares. 20
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Two Dimensional Diagramiii) Circles Here the data values are proportional to the area of the circle. Area of the circle is proportional to the squares of the radius. One has to divide the values of the items by ∏ and then take the square root to find the radius of the circles. Select a suitable scale to draw the circles. 21
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Two Dimensional Diagram iv) Pie diagram Pie diagram are very popular to show relative changes in terms of percentage break down of different components. Examples: percentage shares of different sectors of economy in the group of the states. Steps for Construction Work out the percentage share of different components Convert the percentage share into corresponding degrees on the circle by multiplying with 360/100. 22
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Two Dimensional Diagramiv) Pie diagram Draw a circle of appropriate size with a compass. Size depends upon the available space and other factors of presentation. Use different colours or shades to distinguish different components. Generally while cutting sectors in the circle the largest sector (representing the largest component) should be drawn at 12 O’clock position in the circle and other components sectors are placed in clock wise manner in descending orders of magnitude. 23
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Fig. 3.7 Percentage Composition ofpopulation by age Group: 2001 Census JHARKHANDA ORISSA CHATISHGARH 60+ 60+ 60+ 0 -14 0 -14 0 -14 15 -59 15 -59 15 -59 24
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Three - Dimensional Diagrams (Volume diagram): In such diagram three dimensions – length, breadth and height are taken into consideration and diagrams are show constructed that their volumes are proportional to the values of the items. Cubes, Cylinders and spheres are usually used to re-present data in this category. 25
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Pictographs or pictorial diagrams: Pictographs are very popularly used in presenting statistical data. In this category actual pictures are used to depict the kind of data being dealt with. Population of OrissaYear 1951 1961 1971 1981Population 14 18 22 26(in million) Source: Census of India, 1961 – 2001 26
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Population of OrissaYear195119611971 1981 27 Source: Census of India, 1961 – 2001
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Cartograms (Statistical Maps) Geographical comparison of data These are uses to give quantitative information on a geographical basis. The quantities on the map can be shown in Many ways, such as through shades or colours by dots, by placing pictograms or actual figures in each. LOOK AT THE DATA 28
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M ap 3.2 Distri cts of Orissa Classified according toPrevale nc e of Hearing Disa bility per lakh population : Census 2001 Sundarg ar h Mayurbhanj Jharsug uda Keonjhar Sam balpur Deog ar h Balasore Bargarh Sonepur Bhadr ak Dhenkanal Angul Jajpur Nuapada Bolangir Boudh Kendrapara Cuttack Nayagar h Khurda Jagatsingpur Kandham al Puri Nabrangpur Kalahandi Ganjam Rayagada Gajapati Koraput Pre vale nc e of hearing disabilityMalkang iri 140 - 22 0 221 - 25 4 255 - 31 4 Data Source: Deriv ed from Dis ability data from Census ,2001
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Map 3.6 Districts of Orissa Classified according to Prevalence of Mental Disability per lakh population : Census 2001 Sundargarh Mayurbhanj Jharsuguda Keonjhar Sambalpur Deogarh Balasore Bargarh Sonepur Bhadrak Angul Dhenkanal Jajpur Nuapada Bolangir Boudh Kendrapara Cuttack Nayagarh Khurda Jagatsingpur Kandhamal Puri Nabrangpur Kalahandi Ganjam Rayagada Gajapati Koraput Prevalence of mental disability 175 - 227Malkangiri 232 - 292 303 - 413 Data Source: Derive d from Disability da ta from C ensus ,2001 Map not to sc ale
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GRAPHSBroadly various graphs can be classified under the following two headsa) Graphs of time series,b) Graphs of frequency distributions. GRAPHS OF TIME SERIES Values of the variable observed at different point of time give rise to a time series. Time series presented graphically becomes extremely helpful in studying changes 31 over time. Such graphs are most
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GRAPHS Contd.Technique of construction of time series graph Time is taken on the X-axis (horizontal) and the variable on the Y-axis (vertical) of the graphs. The unit of time i.e. calendar year or financial year and unit of measurement of the variable should be clearly stated. Generally begin Y-axis with zero and select a suitable scale so that the entire data is accommodated in the space available. 32
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GRAPHS Contd.Technique of construction of time series graph On the arithmetic scale magnitude is represented by equal distance. Time period vrs. the values of the variables are plotted in the graph paper. Points so obtained are joined with straight lines (not with curves). If in one graph more then two variables are plotted they should be distinguished by thin , thick dotted lines etc., 33
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Graph of one variable: When only one variable is to be represented. GRAPH OF TWO OR MORE VARIABLES:-If the unit of measurement is same we can represent two or more variables on the same graph and different lines are distinguished by plotting thick, thin , dotted, broken lines etc… 34
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GRAPH HAVING TWO SCALES:- If two variables are expressed in two different units, then we will have two scales - one on the left and the other in the right. To facilitate comparison each scale is made proportional to respective average of each. The average values of both the variables are kept in the middle of the graph and then scales are determined. 35
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RANGE CHART:- Shows the range of variation, i.e. the minimum and maximum values of variable for example minimum and maximum temperature for different time period can be depicted with range chart.Constructing Range Chart Take time on the X-axis and the variables on the Y-axis. Draw two curves by plotting the given data- one curve representing the lowest value and the other curve representing the highest value 36
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LOOK AT THE DATA Trend of Sex Ratio of SCs and STs of Orissa, 1961 - 2001 ScheduledCensus Scheduled Castes Tribes Others Year Orissa Orissa Orissa R U T R U T R U T 1961 1020 930 1015 1018 946 1016 1013 779 991 1971 996 955 993 1009 958 1007 1000 821 979 1981 992 951 988 1015 947 1012 994 837 969 1991 981 932 975 1006 930 1002 983 849 959 2001 983 949 979 1006 948 1003 980 881 960Source: Census of India: 1961 -2001 37
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Fig. 3.8 Trend of Sex Ratio of SCs and STs of Orissa, 1961 - 20011010980950 1961 1971 1981 1991 2001 SCs STs Others 38
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Fig. 3.9 Trend of Rural – Urban difference in Sex Ratio of Orissa by Social Groups, 1961 - 2001 245 220 195 170 145 120 95 70 45 20 1961 1971 1981 1991 2001 SCs STs Others 39
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Table 3.2 Age specific sex ratio in Orissa by social groups: 1961—2001Age Group Social Groups 1981 1991 2001 EXERCISE: Look 0-14 SCs 992 1035 964 at the data and STs 999 998 959 try to understand Others 995 959 955 it through 15-49 SCs 994 963 982 STs 1011 1013 1012 diagrams and Others 953 970 962 graphs and 50-59 SCs 868 898 996 interpret. STs 935 914 1012 Others 881 946 942 60+ SCs 1062 887 1012 STs 1247 1044 1203 Others 1024 978 981 All ages SCs 988 975 979 STs 1012 1002 1003 Others 969 959 960Source: Census of India, Social & Cultural Table, 1961, 1971, 1981, 1991& age-data Census-2001 40
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FREQUENCY GRAPHS Histogram Frequency polygon Smoothed frequency curve Cumulative frequency curve or ogives. 41
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