Insights into Graphical Representation of Data in Business Mathematics

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Graphical representation of data in Business Mathematics is a powerful tool that provides a bird's eye view of statistical information. It enables easy visualization of variations in variables, aiding in understanding time series and frequency distributions efficiently. While graphs offer quick estimation and identification of median and mode values, they can sometimes be less significant and might lead to wrong conclusions. Comparing graphs with diagrams, where graphs are more suitable for precise value determination but lack attractiveness. It's essential to provide a clear heading and choose an appropriate scale for effective data presentation.

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Class B.Com-II semester Subject-Business Mathematics Topic-Graphical Representation of Data Prepared By Ms.Bhanu Sachdeva (Assistant Professor) Department- Commerce and management College-I.B(PG) college Panipat,Affiliated to Kurukshetra University,Kurukshetra

In this method,Agraph is used to show the variations in a variable by means of a curve or a straight line with respect to some characteristics Graphic presentation is another method of data presentation. In this method,statisticaldata is presented on the graph paper Graphs give bird s eye view to the whole statistical data that have been collected about any problem.

Presentation of time series and frequency distribution:Graphic presentation is a very effective technique of data presentation in case of times series data and frequency distributions. Saving of time:Less time is required to plot points and connect them with lines than to draw the diagrams as in the case of diagrammatic representation. Easy estimation: Graphic presentation facilities interpolation and extra polation of data in a more convenient and precise manner Values of median and mode:The values of median,mode etc.canbe ascertained with the help of graphs . Variations in the values:With the help of graphs,we can study the variations in the values of variables.

Less significant :Graphs are not of equal significance to all the people.It is generally difficult for a layman to interpret graphs. Only a measure of tendency:Graphs show only tendency of the data. Actual values are not always clear from the graphs. Lack of precise value :since graphs are based on brief information,thesedo not show precise values . Wrong conclusions:Graphs may some times suggest wrong conclusion.infact even a small change in the scale of the graph causes a lot of difference in the structure of the graph.This may lead to wrong conclusion.

Construction A diagram is generally constructed on a plain paper. Mathematical relationship A diagram does not represents mathematical relationship between two variables. Determination of values Diagrams are not used to obtain the values of mode, median etc. Construction A graph is generally constructed on a graph paper. Mathematical relationship A graph does not represents mathematical relationship between two variables. Determination of values Graphs are used to obtain the values of mode, median etc. Attractive and impressive Graphs are notattractive and impressive Attractive and impressive Diagrams are attractive and impressive

Heading:Everygraph must have a suitable and precise heading. Heading must be self explanatory about the nature of information in the graph. Choice of scale: One should fix an appropriate scale on which data should be presented.The graph should be on the middle of the graph paper to make it attractive . Method of plotting the graph:onthe X-axis ,the points are plotted from left to right and on the Y- axis the points are plotted upward from bottom to top. Lines of different types:Ifmore than one line or curve are to be drawn in the same graph then these lines should be distinguished from each other in the form of broken lines(-----),dotted lines( ..)etc. Use of false base line:If the values in a series are very large and the difference between the smallest value and zero is high then a false base line is drawn. Table of data:Itwould be useful to give the table of data along with the graph of data. This helps in the verification of the curve. To draw a line or curve:we mark different points on the graph paper.These points are joined to make a line or curve. The joining line must be uniform throughout its length.Itshould not be of different thickness of its different points.

Line graphs:Linegraphs are used to show how a quantity changes continuously.If the line goes up,the quantity is increasing;if the line goes down, the quantity is decreasing and if the line is horizontal,we conclude that there is no change in the quantity.

Example:constructa line graph for the following data Years 2015 2016 2017 2018 2019 Production( 000 tonnes) 400 430 412 407 422 Solution:Linegraph showing production from 2015 to 2019 is as given in the following figure

435 430 Production( 000 tonnes) 425 420 415 410 405 400 395 390 385 2015 2016 2017 2018 2019

Example:Construct a line graph for following data Years 2013 2014 Production of firm A( 000 tonnes) 2015 2016 2017 2018 16.8 16.2 15.2 18.8 20.5 19.8 Production of firm B( 000 tonnes) 20.5 18.2 14.8 12.6 15.5 16.4 Solution:Graph showing production of firm A and B from 2013 to 2018 is as given in the following figure

40 35 Production of firm A and B 30 25 Firm B 20 Firm A 15 10 5 0 2013 2014 2015 2016 2017 2018

Example: construct a band graph for the data given below Production(million tons) Production(million tons) Year A B C D TOTAL 2011 12 8 9 15 44 2012 13 9 9 14 45 2013 15 6 8 18 47 2014 17 10 10 18 55 2015 18 12 12 14 56 2016 20 12 16 12 60 2017 22 9 14 19 64

Solution:Band graph showing production in different years is as given below. for plotting ,first line shows production of commodity A , second line shows production of commodity B, Third line shows production of commodity C, fourth line shows production of commodity D Production(million tons) Production(million tons) 70 60 50 D 40 C 30 B 20 A 10 0 2011 2012 2013 2014 2015 2016 2017

The area below yellow line represent the production of commodity A. The area between yellow and blue line represent the production of commodity B.The area between blue and red line represents the production of commodity C and the area between red and green line shows the production of commodity D.

Histogram is a graphical representation of a continuous grouped frequency distribution in terms of bars or rectangles of equal width Method of drawing a histogram I. Mark all the class intervals along the X-axis on a suitable scale. II. Mark the frequencies along the Y-axis. III. Construct rectangles of equal width,with the class intervals as bases and heights proportional to their frequencies. IV. The graph containing all these rectangles is called a histogram.

Example:Represent the following data by histogram Marks : 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No.of students: 10 20 25 10 8 5 2 Solution:we represent the marks (class intervals) along the X-axis and frequencies (no.of student )along the Y-axis with a suitable scale.