Grouped data are often represented graphically by histograms. A histogram consists of rectangles, each of which has breadth equal or proportional to the size of the concerned call interval, and height equal or proportional to the corresponding frequency. In a histogram, consecutive rectangles have a common side. For this, the class intervals are made overlapping in all cases.
Method of constructing a histogram:
Step I: Observe the class intervals of the distribution. If they are nonoverlapping (discontinuous), Change them into overlapping (continuous) classes.
Step II: Locate the class boundaries on the xaxis (horizontal axis).
Step III: Construct a vertical rectangle on each line segment representing a class interval such that the height of the rectangle represents frequency of the class interval.
Step IV: Put a kink mark (N) on the horizontal axis, between the vertical axis and the first rectangle if the leftmost rectangle does not have the vertical axis on its side.
Note: For drawing graphs, a scale of representation is required. Unless given, the choice of scale is made of suit the data.
Different scales can be taken for the two axes.
In the scale for the xaxis is “1 mm = an interval of 5” then the class interval 20 – 40 will be shown by 4mmlong line segment on the xaxis.
If the scale for the yaxis is “1 mm = frequency 1” (i.e., frequency of 1 is denoted by 1 mm) then the frequency 10 will be shown by 1cmlong line segment on the yaxis.
Example: Construct a histogram for the following frequency distribution.
Height (in cm) 
101
– 110 
111
– 120 
121 – 130 
131 – 140 
141 150 
Number
of children 
15 
18 
12 
6 
9 
Solution:
Here, the distribution is discontinuous. So, first we write the frequency distribution with overlapping intervals to make it continuous.
Height (in cm) 
100.5110.5 
110.5–120.5 
120.5–130.5 
130.5–140.5 
140.5150.5 
Number
of children 
15 
18 
12 
6 
9 
Following the abovementioned steps, the histogram will be as shown below.
Scale: On the xaxis, 1 cm = height of 10 cm.
On the yaxis, 0.5 cm = frequency 3.
Utility of Histograms
A histogram for a frequency distribution displays the frequencies of different class intervals. As such it becomes easier to locate the class interval having the greatest frequency or the least frequency. Histograms also help to find the mode of a distribution.
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