Presentation of data

• 1. Thediagrams should be simple. Each diagram must be given a clear,concise and suitable title withoutdamaging clarity. A proper proportion between height andwidth must be maintained in order toavoid an unpleasant look. Select a proper scale; it should be ineven numbers or in multiples of five orten.e.g. 25,50, 75 or 10, 20, 30, 40, ....etc. But no fixed rule.samta soni 4/9/20131

2. In order to clear certain points, always putfootnotes. An index, explaining different lines, shadesand colors should be given. Diagrams should be absolutely neat andclean. "The important point that must be borne inmind at all times that the pictorialrepresentation chosen for any situation mustdepict the true relationship and point out theproper conclusion. Above all the chart mustbe honest." .... C. W. LOWE. samta soni 4/9/2013 2 3. Graphics, such as maps, graphs and diagrams, are used torepresent large volume of data.They are necessary: If the information is presented in tabular form or in a descriptiverecord, it becomesdifficult to draw results. Graphical form makes it possible to easily draw visual impressionsof data. The graphic method of the representation of data enhances ourunderstanding.samta soni 4/9/20133 4. It makes the comparisons easy. Besides, such methods create an imprint on mind for a longer time. It is a time consuming task to draw inferences about whatever isbeing presented innongraphical form. It presents characteristics in a simplified way. These makes it easy to understand the patterns of populationgrowth, distribution andthe density, sex ratio, agesex composition, occupational structure,etc. samta soni 4/9/2013 4 5. Selectionof a Suitable Graphical MethodEach characteristic of the data can only besuitably represented by an appropriategraphical method. Selection of Suitable ScaleEach diagram or map is drawn to a scalewhich is used to measure the data. The scalemustcover the entire data that is to berepresented. The scale should neither be toolarge nor toosmall. DesignT itle,Legend or Index,Direction samta soni 4/9/2013 5 6. Diagrams and Graphs are meant for a layman. Tables are meant for statisticians for thepurpose of further analysis. Diagrams give only an approximate idea. Tables contain precise figures. Exactvalues can be read from tables.samta soni 4/9/2013 6 7. Diagrams can be more easily compared, and canbe interpreted by a layman. Comparison and interpretations of tables can onlybe done by statisticians and it is a difficult task.Diagrams and graphs cannot present muchinformation. Tables can present more information. Diagrams are more attractive and have a visualappeal. Tables are dry for a layman ( may be attractive to astatistician.) samta soni 4/9/2013 7 8. Presentation of Quantitative Data by graphs Histograph Frequency polygon Line chart or graph Cumulative frequency diagram Scatter or dot diagramsamta soni 4/9/20138 9. Presentation of Qualitative Data Bar diagram Pie or sector diagram Pictogram Map diagram or spot mapsamta soni 4/9/20139 10. PurposeTo graphically summarize the distributionof a univariate data set. 40 35 35 30 3025 2520 20Series1 Linear (Series1)15 1510 105500 samta soni4/9/2013101-110 111-120 121-130 131-140 141-150 151-160161-170 171-18010 11. Specialform of Bar diagram whichrepresent categories of continuous andordered data. It consists of a series of bars and blocks. The class interval are given along thehorizontal axis and the frequency along thevertical axis. The width of bar represents the interval ofeach category.samta soni 4/9/201311 12. The histogram graphically shows thefollowing: Center (i.e., the location) of the data; Spread (i.e., the scale) of the data; Skewness of the data; Presence of outliers; and Presence of multiple modes in the data. samta soni 4/9/2013 12 13. It is an area diagram. X axis depicts the category of data and yaxis depicts the frequency of data in eachcategory. Frequency polygon can be obtained fromhistogram by joining midpoints of blocksor rectangles of the histogram. It can be more useful than the histogrambecause several frequency distributionscan be plotted on one graph. samta soni 4/9/2013 13 14. samta soni 4/9/201314 15. It is used when sets of data are to beillustrated on the same diagram suchas death and birth rates. Frequency polygons are a graphicaldevice for understanding the shapes ofdistributions. They serve the samepurpose as histograms, but areespecially helpful in comparing sets ofdata. Frequency polygons are also agood choice for displaying cumulativefrequency distributions. samta soni 4/9/2013 15 16. Frequency distribution curves are like frequency polygons. Infrequency distribution, instead of using straight line segments, asmooth curve is used to connect the points.samta soni 4/9/2013 16 17. Asmooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes very large.samta soni 4/9/2013 17 18. Shape of Distribution Curves:- (i) Symmetrical or bell-shaped (ii) Moderately symmetrical or skew (ii) J-shaped and (iv) U-shaped.samta soni 4/9/201318 19. Histogram is a bar graph while frequencypolygon is a line graph. Frequency polygon is more useful andpractical. In frequency polygon it is easyto know the trends of the distribution;unable to do so in histogram. Histogram gives a very clear and accuratepicture of the relative proportion of thefrequency from interval to interval.samta soni 4/9/2013 19 20. It is used to show the trends of events withthe passage of time. It is a frequency polygon presentingvariations by a line .the class interval canbe a week, a year or 100year. A line graph is useful for displaying dataor information that changes continuouslyover time. samta soni 4/9/2013 20 21. Theline graphs are usually drawn to represent the time series data related to the temperature, rainfall, population growth, birth rates and the death rates.samta soni 4/9/201321 22. The various parts of a line graph. TitleThe title of the line graph tells us what the graph is about. LabelsThe horizontal label across the bottom and the verticallabel along the side tells us what kinds of facts are listed. ScalesThe horizontal scale across the bottom and the verticalscale along the side tell us how much or how many. PointsThe points or dots on the graph show us the facts. LinesThe lines connecting the points give estimates of thevalues between the points.samta soni 4/9/2013 22 23. Polygraph is a line graph in which two ormore than two variables are shown on asame diagram by different lines. It helps incomparing the data. Examples which can beshown as polygraph are: The growth rate of different crops likerice, wheat, pulses in one diagram. The birth rates, death rates and lifeexpectancy in one diagram. Sex ratio in different states or countries inone diagram. samta soni 4/9/201323 24. samta soni 4/9/201324 25. samta soni 4/9/201325 26. The line and bar graphs as drawnseparately may also be combinedto depict the data related to someof the closely associatedcharacteristics such as theclimatic data of mean monthlytemperatures and rainfall.samta soni 4/9/201326 27. Multiple bar diagrams are constructed to represent two or more than two variables for the purpose of comparison. For example, a multiple bar diagram may be constructed to show proportion of males and females in the total, rural and urban population or the share of canal, tube well and well irrigation in the total irrigated area in different states.samta soni 4/9/201327 28. samta soni 4/9/201328 29. The curve obtained by plotting cumulating frequencies is called acumulative frequency curve or an ogive.samta soni 4/9/201329 30. 1)Add up the progressive totals offrequencies, class by class, to get thecumulative frequencies. 2) Plot classes on the horizontal ( x-axis )and cumulative frequencies on the vertical( y-axis). 3) Join the points by a smooth curve. Ogives start at (i) zero on the vertical axis, (ii) outside class limit of the last class.samta soni 4/9/2013 30 31. AScatter Diagram examines the relationships between data collected for two different characteristics. Although the Scatter Diagram cannot determine the cause of such a relationship, it can show whether or not such a relationship exists, and if so, just how strong it is. The analysis produced by the Scatter Diagram is called Regression Analysis. samta soni 4/9/2013 31 32. Use a Scatter Diagram to determine if there is correlation between two characteristics. Correlation implies that as one variable changes, the other also changes. Although this may indicate a cause and effect relationship, this is not always the case, since there may be a third characteristic (or many more) that are actually the cause, and both the characteristics of interest are the effect.samta soni 4/9/201332 33. samta soni 4/9/201333 34. Ascatter diagram is a tool for analyzingrelationships between two variables. Onevariable is plotted on the horizontal axis andthe other is plotted on the vertical axis. Scatter diagram is used to prove or disprovecause-and-effect relationships. Examination of theories about cause-and-effect relationships and to search for rootcauses of an identified problem. Scatter diagram used to design a controlsystem to ensure that gains from qualityimprovement efforts are maintained. samta soni 4/9/2013 34 35. Scatterdiagrams will generally show one ofsix possible correlations between thevariables:1.Strong Positive Correlation The value of Yclearly increases as the value of X increases.2.Strong Negative Correlation The value of Yclearly decreases as the value of X increases.3.Weak Positive Correlation The value of Yincreases slightly as the value of X increasessamta soni 4/9/2013 35 36. 4.Weak Negative Correlation The value of Ydecreases slightly as the value of Xincreases.5.Complex Correlation The value of Yseems to be related to the value of X, butthe relationship is not easily determined.6.No Correlation There is no demonstratedconnection between the two variables.samta soni 4/9/2013 36 37. samta soni 4/9/201337 38. samta soni 4/9/201338