Graphical Representation of Data (Line Graph, Bar Diagram & Histogram)


Data Representation

Graphical Representation of Data: Part 1
(Diagrammatic Data Representation: Line Chart, Bar Diagrams and Histogram)

Graphical Representation of Data / Variables

Ø  The data presentation in statistics may be Numerical or Graphical.

Ø  If the data is presented in the numerical form, it will not attract the attention of the audience.

Ø  In order to attract the attention of the audience, Graphical Representation method is usually adopted.

Ø  Graphical Representation: It is the representation or presentation of data as Diagrams and Graphs.

Ø  The statistical graphs were first invented by William Playfair in 1786.

Ø  In graphical data representation, the Frequency Distribution Table is represented in a Graph.

Advantages of Graphical Representation of Data

Ø  Data are presented pictorially.

Ø  Give better insight and understanding of the data.

Ø  Makes the presentation eye-catching.

Ø  The data become more logical (clear).

Ø  The comparison becomes easy.

Ø  Can derive the conclusion from data very quickly.

Ø  Give the spread of the data.

Ø  Reduce space for data representation.

Ø  Helpful in statistical analysis.

Disadvantages of Graphical Representation of Data

Ø  A graph cannot represent all details of the variables.

Ø  Very difficult to include and study the small differences in large measurements.

Ø  Graphs usually show approximate figures.

Ø  Graphs are only a supplement to the tabular presentation of data.

Ø  Graphs cannot be an alternative to tabular presentation.

Ø  Further processing and analysis of data are not possible with graphs.

Things to remember in Graphical Representation Methods

Ø  A graph should have a self-explanatory heading.

Ø  If more than one graph is used in the study, all graphs should be numbered chronologically.

Ø  The scales should be indicated.

Ø  Sketches should be neat and clear

Ø  Footnotes should be given below the graph.

Ø  The size of the graph should fit in the size of the paper / PPT slide.

Ø  Contrasting colours or shades should be used to separate different classes.

Methods of Graphical Representation of Data

Ø  In statistics, the data can be presented graphically using many methods.

Ø  Important graphical representation methods are given below:

(1).      Line Diagram

(2).      Bar Diagram

(3).      Histogram

(4).      Frequency Polygon

(5).      Frequency Curve

(6).      Pie Chart (Circle Diagram)

(7).      Ogive

(1). Line Diagram

Ø  The line diagram is the simplest method of graphical representation.

Ø  In line diagram, the data is represented in the form of straight lines.

Ø  Each line in the diagram represents an observation or a class.

Ø  The height of the line denotes the magnitude of the observation / class.

Ø  The distance between the lines is kept uniform.

Ø  Advantages of line diagram: quick and simple method, comparison become easy.

Example: A study on the number of accidents in the year 2015 in a particular area is given below. Draw a line graph to represent the data.

line diagram data

Solution

line diagram

(2). Bar Diagram

Ø  Bar diagram is also called as bar chart

Ø  A common and simple method of graphical representation of data. 

Ø  Bar diagram is a chart that presents grouped data with rectangular bars.

Ø  Each rectangular bar represents a class.

Ø  Height of the bar is proportional to the magnitude of the item in the class

Ø  Bars are drawn vertically or horizontally with equal spacing between them.

Ø  The width of the bars and the space between them are kept constant.

Ø  The vertical bar diagram is also called as column bar chart.

Ø  In a vertical bar diagram, the independent variables are shown on the X axis, while the dependent variables are shown on the Y axis.

Ø  Bar diagram is further divided into FOUR types:

(a). Simple bar diagram

(b). Multiple bar diagram

(c). Subdivided bar diagram

(d). Percentage bar diagram

(a). Simple bar diagram

Ø  Items are to be compared with respect to a single characteristic.

Ø  Simple bar diagram may be vertical or horizontal.

Example: Draw a simple bar diagram using the following data.

simple bar diagram data

Solution

What is Vertical Bar Diagram

(b). Multiple bar diagram

Ø  Contain two or more bars arranged side by side.

Ø  Allow comparison of multiple sets of variables comparison.

Ø  Different colors or shades are used to distinguish different bars in a single set

Example: Draw a bar diagram using the following data showing the pass percentage of different subjects in five years

what is multiple bar diagram

Solution

Multiple Vertical Bar Diagram

(c). Subdivided bar diagram

Ø  Also called component bar diagram

Ø  The individual bar is subdivided into various parts or compartments.

Ø  The size of various compartments is proportional to the magnitude of the variables.

Ø  Different colours or shades are used to distinguish the compartments of the bar.

Ø  The distance between the bar and the width of the bar is kept constant.

Example: Number of science graduate students in a college is given below. Draw a subdivided bar diagram using the following data.

data subdivided bar diagram

Solution

subdivided bar diagram



(d). Percentage bar diagram

Ø  Percentage bar diagram is a diagram which exhibits a simple analysis of statistical data in terms of percentage.

Ø  The length of all bars is kept constant (100%).

Ø  Each bar consists of several compartments.

Ø  The size of each compartment of a bar corresponds to the percentage of that component with respect to the total.

Example: Draw a percentage bar diagram using the following data.

percentage bar diagram data

Solution: Conversion of absolute values into percentage.

percentage bar diagram data

percentage bar diagram

(2). Histogram

Ø  Histogram is used in the graphical representation of frequency distribution.

Ø  Here each class of the frequency distribution is represented as columns.

Ø  The height of the column corresponds to the magnitude of the frequency.

Ø  A histogram quickly tells how many items are there in each numerical category.

Ø  The histogram resembles a bar diagram (but with a difference).

Ø  In the histogram, the columns representing each class are in close contact and there is no space between them.

Ø  The absence of inter-bar space denotes the continuity of classes in the histogram.

Construction of a Histogram

Ø  The class intervals are taken on the X axis.

Ø  Corresponding frequencies are taken on the Y axis.

Ø  Class intervals used are usually of equal width.

Ø  The frequency is proportional to the area and height of the bar.

Example: Construct a histogram using the following data

how to draw histogram

Solution:

Histogram

Importance of histogram

Ø  The area of blocks in the histogram clearly shows the frequency of each class.

Ø  Histogram shows the spread of observations (uniformly spread or randomly spread or showing central tendency).

Ø  Provide information about skewness or symmetry of data.


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