### Presentation of Data

 Presentation of Data: Diagram attracts the human mind more, compared to numerical figures, which causes one to pause for a while to have a glance at the diagram and thus can get an overall ideas of the said data. In practice a very large variety of diagrams are in use and new ones are constantly being added. In the following only more frequently used diagram are discussed. 1. One Dimensional: The one dimensional representation of data includes different types of bar diagram. a) Simple Bar Diagram: To draw a simple bar diagram, equidistant bars each of equal width are drawn on a line, one for each group of data. The value of each group is represented by the height of the corresponding bar generally, in case of time based data, vertical bars are drawn and to represent space based (or other) data horizontal bars are drawn. A simple bar diagram is used to represent only one variable. b) Sub Divided Bar Diagram: The sub divided bar diagram is used if the total magnitude of the given variable is to be divided into various parts or components. The method of drawing this type of diagram is same as that of the bar diagram, only the bar drawn should be divided into various segments, according to the given components of the total. c) Multiple Bar Diagram:  To represent two or more numerical characteristic by the same diagram, multiple bar diagram is to be used. A multiple bar diagram is obtained by drawing a number of equidistant vertical set of bars on a line. Each set of bars contain two or more adjacent bars. Width of the bars is same and height of the corresponding bars is to be taken in the ratio of the numerical figure which is denoted by that bar. The total numbers of set of bars are taken to be equal to the total number of items. d) Percentage Bar: Percentage bars are particularly useful in statistical work which requires the portrayal of relative changes in data. When such diagrams are prepared the length of the bars is kept equal to 100 and segments are cut in these bars to represent the components (percentage) of an aggregate. e) Deviation Bar:  Deviation bars are popularly used for representing net qualities – excess or deficit, i.e. net profit, net loss, net export or imports etc. such bars can have both positive and negative values. Positive values are shown above the bars line and negative values below it. 2. Two Dimensional: In two dimensional diagrams, the length as well as the width of the bars is considered. Thus the area of the bars represents the given data. Two dimensional diagrams are also known as surface diagram or area diagram. The important types under this category are- a) Rectangles: In constructing rectangle one may represent the figures as they are given or may convert them to percentage and then subdivide the length into various components. The area of a rectangle is equal to the product of its length and width, so in constructing a rectangle both length and width are important. b) Squares: The rectangular method of diagrammatic presentation does not look good when the values of item vary widely. So, in order to overcome this difficulty squares method are used. In this method one has to take the square root of the values of various items that are to be shown in the diagrams and then select a suitable scale to draw the square. c) Circles: In Circles both the total and the component parts or sector can be shown. Since the area of a circle is preoperational to the square of its radius, so in the construction of circles, the square root of various figures are worked out, and the radii of the circles drawn are proportional to the square root of the figures. d) Pie Diagram: For constructing a pie diagram the various components values of data are transposed into corresponding degrees on the circle, and then the diagram obtained by dividing a circle into various sector is known as circle or pie diagram. The number of sector should be equal to the total number of components parts. The area of the sectors should be taken in the ratio of the values of the constituent parts. 3. Three Dimensional: Three dimensional diagrams are also known as volume diagrams. In such diagram, three things namely length, width and height have to be taken into account. Such diagrams are used where the range of difference between the smallest and the largest values is very large. It includes cube, cylinder and sphere. Amongst three dimensional diagram, cubes are most popular and also simple to draw. The side of a cube is drawn in proportional to the cube root of the magnitude of data. 4. Others: Some other tools that can be used to represent data are - a) Pictographs: Pictures are attractive and easy to comprehend and as such this method is particularly useful in presenting statistics to the layman.  In pictograph the data are represented through a pictorial symbol, which is very carefully selected, so pictographs depict the kind of data we are dealing with. b) Cartogram: Cartograms or statistical maps are used to give quantitative information on a geographical basis. They thus represent spatial distributions. The quantities on the map can be shown in many ways, such as through shades or colors, by dots, by placing pictograms in each geographical unit and by placing the appropriate numerical figures in each geographical unit. c) Graphs: When we observe the values of a variable at different points of time, the series so formed is known as time series. Time based data can be represented by line diagram. In this case, points are plotted on the graph paper by taking time as X co-ordinate and the data corresponding to that particular time as Y co-ordinate. After that, by joining the points in pairs by line segment, line diagrams are drawn. d) Histogram: Histogram consists of a series of adjacent vertical rectangles, drawn and each of each class intervals. Area of each rectangle determines the frequency of that class. Generally for the graphical representation of frequency distribution of continuous variable histogram is used. To draw histogram, firstly class intervals are marked along horizontal axis (X-axis) and frequencies are to be marked along vertical axis (Y-axis) after that taking, difference between lower and upper boundaries as base rectangles are drawn one for each class recording to the ratio of the area of the frequency. Since the area of the rectangles having same base are proportionate to the length, therefore, in case of frequency distribution having equal class width, the height of the rectangles should be taken in the ration of the frequencies. e) Frequency Polygon: To draw frequency polygon, points are plotted on the co-ordinate plane by taking the mid value of a class as X co-ordinate and corresponding frequency of the class as Y co-ordinate. The points are then joined in pairs represented by a line segment. The polygon is closed at both ends, by extending it to the mid-points of two classes having frequency zero, before the first class and after the last class. f) Smoothed Frequency Curve: The smoothed frequency curve is drawn freehand in such a manner that the area included under the curve is approximately the same as that of the polygon. The object of drawing a smoothed frequency curve is to eliminate as far as possible accidental variations that might be present in the data. g) Cumulative Frequency Curves or “Ogives”: Cumulative frequency curve is a smooth curve. To draw this curve, points are plotted on the graph paper by taking upper class boundaries as X co-ordinate and cumulative frequency of the respective class as Y co-ordinate. The points so obtained are joined by a smooth free hand curve. This curve is joined to the lower class boundary of the first class. The smooth curve drawn in this manner is called the cumulative frequency curve.