This is a form of representation like the bar graph, but it is used for continuous class intervals.
For instance, consider the frequency distribution Table 14.6, representing the weights of 36 students of a class:
Let us represent the data given above graphically as follows:
(i) We represent the weights on the horizontal axis on a suitable scale. We can choose the scale as `1 cm = 5 kg`. Also, since the first class interval is starting from `30.5` and not zero, we show it on the graph by marking a kink or a break on the axis.
(ii) We represent the number of students (frequency) on the vertical axis on a suitable scale. Since the maximum frequency is `15`, we need to choose the scale to accomodate this maximum frequency.
(iii) We now draw rectangles (or rectangular bars) of width equal to the class-size and lengths according to the frequencies of the corresponding class intervals.
For example, the rectangle for the class interval `30.5 - 35.5` will be of width `1` cm and length `4.5` cm.
(iv) In this way, we obtain the graph as shown in Fig. 14.3:
Observe that since there are no gaps in between consecutive rectangles, the resultant graph appears like a solid figure. This is called a histogram, which is a graphical representation of a grouped frequency distribution with continuous classes.
Also, unlike a bar graph, the width of the bar plays a significant role in its construction.
Here, in fact, areas of the rectangles erected are proportional to the corresponding frequencies.
However, since the widths of the rectangles are all equal, the lengths of the rectangles are proportional to the frequencies. That is why, we draw the lengths according to (iii) above.
Now, consider a situation different from the one above.