Introduction to graphical representation of data:
Any collection of information in the form of numerical figures giving the required information is called a data. There are many ways for the graphical representation of data. They are
- Bar Graphs
- Frequency Polygons
- Histograms
- O give
- Pictographs
- Pie charts
In this article, let us discuss about Histogram and frequency polygons for graphical representation of data. Also let us graph related to day – to – day use like student marks. Other form of graphs are beyond the scope of the present article.
Histogram - Graphical Representation of Data :
The histogram of a frequency data consists of a number of rectangles erected on the class intervals of the distribution. The area of the rectangle are proportional to the frequencies of the respective classes. Usually the class intervals are marked successively along the X-axis and the frequencies are marked along the Y-axis. Our assumption is that the sum of the areas of all the rectangles of the histogram is the same as the total frequency.
Example for Histogram(Graphical Representation):
Represent the marks of the students by means of the histograms
| Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Number of Students | 4 | 6 | 8 | 10 | 7 | 5 |
Solution:
We know that when two mutually perpendicular axes are drawn on a graph paper four quadrants are formed.
- To draw a histogram we need only one quadrant namely the first quadrant since the class intervals and the frequencies are positive numbers.
- Hence take the X-axis along the bottom horizontal line and the Y-axis along the left extreme vertical line on the graph paper.
- Mark the class intervals continuously along the X-axis by taking a suitable scale.
- Identify the maximum frequency in the table and then choose a suitable scale along the Y-axis
Graphical Representation for Histogram:
Graphical Representation of Data Using Frequency Polygon:
- Plot the points on a graph paper taking the mid values of the class intervals as x-coordinates and their corresponding frequencies as y-coordinates.
- Join the points with the help of line segments. We notice that the figure mark the mid point of the class interval preceding the first class interval on the X-axis and join this point corresponding to the midpoint of the first class interval.
- Mark the midpoint of the class interval succeeding the last class interval on the X-axis and join this point with the point corresponding to the midpoint of the last class interval. The closed figure thus obtained is called a frequency polygon.
Example for Graphical Representation of Frequency Polygon:
Construct the frequency polygon for the following data
| Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Number of Students | 4 | 6 | 8 | 10 | 7 | 5 |
Graphical Representation for Frequency Polygon:
