GRAPHICAL REPRESENTATION OF DATA

An attractive representation of a frequency distribution is graphical representation. 

Graphical representation can be used for both the educated section and uneducated section of the society. Furthermore, any hidden trend present in the given data can be noticed only in this mode of representation.

We are going to consider the following types of graphical representation :

1.  Line diagram

2. Histogram

3.  Bar diagram

4.  Pie chart

5. Frequency polygon

6. Ogives or Cumulative frequency graphs

Example 1 :

The profits in thousand of dollars of an industrial house for 2002, 2003, 2004, 2005, 2006, 2007 and 2008 are 5, 8, 9, 6, 12, 15 and 24 respectively. Represent these data using a suitable diagram.

Solution :

We can represent the profits for 7 consecutive years by drawing either a line diagram as given below.

Let us consider years on horizontal axis and profits on vertical axis.

For the year 2002, the profit is 5 thousand dollars. It can be written as a point (2002, 5)

In the same manner, we can write the following points for the succeeding years.

(2003, 8), (2004, 9), (2005, 6), (2006, 12), (2007, 15) and (2008, 24)

Now, plotting all these point and joining them using ruler, we can get the line diagram.

Showing line diagram for the profit of an Industrial House during 2002 to 2008.

Example 2 :

Draw a histogram for the following table which represent the marks obtained by 100 students in an examination :

Solution :

The class intervals are all equal with length of 10 marks.

Let us denote these class intervals along the X-axis.

Denote the number of students along the Y-axis, with appropriate scale.

The histogram is given below.

Example 3 :

The total number of runs scored by a few players in one-day match is given.

Solution :

Draw bar graph for the above data.

Example 4 :

The number of hours spent by a school student on various activities on a working day, is given below. Construct a pie chart using the angle measurement.

Draw a pie chart to represent the above information.

Solution :

The central angle of a component is

= [Value of the component/Total value] x 360°

We may calculate the central angles for various components as follows :

From the above table, clearly, we obtain the required pie chart as shown below.

Example 5 :

Draw a frequency polygon for the following data without using histogram.

Solution :

Mark the class intervals along the X-axis and the frequency along the Y-axis.

We take the imagined classes 0-10 at the beginning and 90-100 at the end, each with frequency zero.

We have tabulated which is given below. 

Using the adjacent table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

We draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ to obtain the required frequency polygon ABCDEFGHIJ, which is given below.

Example 6 :

Draw ogives  for the following table which represents the frequency distribution of weights of 36 students. 

Solution :

To draw ogives for the above frequency distribution, we have to write less than and more than cumulative frequency as given below.

Now, we have to write the points from less than and more than cumulative frequency as given below.

Points from less than cumulative frequency :

(43.50, 0), (48.50, 3), (53.50, 7), (58.50, 12), (63.50, 19), (68.50, 28) and (73.50, 36)

Points from more cumulative frequency :

(43.50, 36 (48.50, 33), (53.50, 29), (58.50, 24), (63.50, 17), (68.50, 8) and (73.50, 0)

Now, taking frequency on the horizontal axis, weights on vertical axis and plotting the above points, we get ogives as given below.

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