There are mainly four graphical representation of frequency distribution, via, (a) Histogram, (b) Frequency polygon, (c) Bar chart, (d) Ogive.

**(a) ****Histogram**. In this graph the sides of the column represent the upper and lower class boundaries and their heights are proportional to the respective frequencies. Consider the following grouped frequency distribution.

The histogram is drawn as follows (Fig. 1.1)

**Note.** If the width of the class intervals are not same then calculate 'Relative frequency density' *(rfd) *for all classes as follows:

* rfd=Frequency/(Total Frequency* class width)*

Then take *rfd *on *y-axis *and class intervals on x-axis to draw histogram.

(b**) Frequency polygon**. Consider the mid-points with a height proportional to class frequency in the histogram. If these points are joined by straight lines then the resultant graph is called frequency polygon.

(c**) Bar chart**. A bar chart is a graphical representation of the frequency distribution in which the bars are centered at the mid-points of the cells. The heights of the bars are proportional to the respective class frequencies.

If a single attribute is presented then it is called simple bar chart (Fig. 1.2). When more than one attribute is presented then it is called multiple bar charts.

**(d) Ogive.** There are two types of cumulative frequency distribution—less than type and more than type which are illustrated in the following table.

Such a cumulative frequency distributions may be represented graphically and the graph is known as ogive because of its similarity to the ogee curve of the architect and the dam designer. The intersection point of the two curves give the median of the distribution.

For grouped frequency distribution, the ' less than' ogive must be plotted against the upper class boundary and not against the class mark, whereas for 'more than' ogive the cumulative frequency must be plotted against lower class boundary.

In this book if the type of the cumulative distribution is not mentioned it is to be understood that it is less than type.