**Graphical Representation of Data / Variables**

**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**

**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**

**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**

**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**

**(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.

*Solution*

**(2). Bar 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**

**(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.

*Solution*

**(b). Multiple 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

*Solution*

**(c). Subdivided 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.

*Solution*

**(d). Percentage 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.

*Solution:* Conversion of absolute values into percentage.

**(2). Histogram**

**(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**

**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

*Solution:*

**Importance of 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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