The following points highlight the top two ways of representing data. The ways are: 1. Tabular Representation of Data 2. Graphic Representation of Data.
Way # 1. Tabular Representation of Data:
Tabulation is a process of orderly arrangement of data into series or rows or columns, where they can be read at a glance. This process may be called as summarisation of data in an orderly manner within a limited space. It helps in simplifying the raw data, comparison can be done easily, reveals the pattern of distribution of any attribute, detects the omissions and errors.
Types of Table:
(a) Simple Table:
In simple table only one character is considered such as length of papaya plant in a field.
(b) Complex Table:
In complex table more than one character is considered such as, length, sex of the plant, disease incidence, etc.
Way # 2. Graphic Representation of Data:
The quantitative and continuous data can be represented graphically by using the following diagrams:
1. Histogram
2. Frequency polygon
3. Frequency curve
4. Cumulative frequency curve
5. Dot diagram
6. Line diagram
7. Bar diagram
8. Pie-chart
Histogram:
This graph is used for continuous frequency distribution. The width of class interval marked along with the X-axis. On this width, rectangles of areas proportional to the corresponding frequencies of the respective class intervals are erected.
If the class intervals are of equal lengths, then the heights of the rectangles are proportional to the corresponding frequencies and for unequal class intervals, the heights of the rectangles are proportional to the ratios of the frequencies to the width of the corresponding class (Fig. 9.2).
Frequency Polygon and Frequency curve:
The values of variables for an ungrouped data are taken on the X-axis and their frequencies are put on the Y-axis. Whereas for grouped data, the mid-point of each class- interval are put on the X-axis and frequency on the Y-axis are put and the dots are joined by straight line is called frequency polygon (Fig. 9.2), and the free hand curved drawing will represent the frequency curve (Fig. 9.3).
Cumulative Frequency Curve:
This curve is drawn with the help of cumulative frequency distribution table. The mid-point of class interval (in case of grouped data), or the values of variable (in case of ungrouped data) are put on the X-axis and their cumulative frequency are put on the Y- axis which represents the cumulative frequency curve (Fig. 9.4).
Dot Diagram:
This kind of diagram is prepared after cross tabulation in which frequencies of at least two variables have been cross classified. One variable being independent and the other variable being dependent. This type of graphic representation shows the nature of correlation between two variable characters, X and Y, of the same individual, such as colour and texture of seed coat of peas, length of pod and number of seeds/pod, etc. (Fig. 9.5).
Example 3:
Lengthy of pod and number of seed/pod are observed in 10 samples.
Line Diagram:
This is the simplest type of diagram where data is represented by the line only following the frequency distribution table. In case of ungrouped data, the values of variables are put on X-axis and the frequency is put on Y-axis, the straight lines are drawn proportional to the frequencies (Fig. 9.6).
Bar Diagram:
This is one dimensional diagram where bars of equal width are drawn either horizontally or vertically which represents the frequency of the variable. The width of bars should be uniform throughout the diagram.
Bar diagram may be of 4 types (Fig. 9.7):
Simple Bar Diagram:
This type of bar diagram is used to represent only one variable by one figure.
Divided Bar Diagram:
When the frequency is divided into different components then the diagrammatic representation is also called a divided bar diagram.
Percentage Bar Diagram:
The total length of bars corresponds to 100 and the divisions of the bar correspond to the percentage to different components.
Multiple Bar Diagram:
When a comparison between two or more related variable? has to be made, then this type of bar diagram becomes essential.
Example 4:
In an investigation, the total cereal crop production is noted in the following table. Make a divided Bar diagram and a percentage bar diagram from the data (Fig. 9.7b, c).
Pie Diagram:
It is an easy way of presenting discrete data of qualitative characters such as colour of flowers, colour of seed coat, texture of seed coat, etc. The frequencies are shown in a circle. Degree of angle denotes the frequency and area of the sector helps to compare at a glance.
Size of the angle is calculated according to following formula:
Size of the angle = Class frequency/Total observation x 360°
Example 5:
In a hybridization experiment, among the F1 hybrid seeds, the following results are observed.
Brown and large — 54
Brown and small — 18
White and large — 18
White and small — 6
Make a pie diagram of this observation (Fig. 9.8).
