Histogram

Out of various methods of presenting a frequency distribution graphically, the histogram is the most popular and widely used in practice. The histogram is a set of vertical bars whose areas are proportional to the frequencies shown.

While constructing a histogram the variable is always taken on the X-axis and the frequencies depending on it on the Y-axis. Every class is then shown by a distance on the scale that is proportional to its class-interval. The distance for each rectangle on the X-axis shall remain the same, in case the class-intervals are throughout uniform. It they are different then they vary. The Y-axis shows the frequencies of each class that constitute the height of its rectangle. In this manner we get a series or rectangles each having a class-interval as its width and the frequency distance as its height. The area of the histogram shows the total frequency as distributed throughout the classes.

The histogram must be clearly distinguished from a bar diagram. The differentiation lies in the fact that where a bar diagram is one dimensional i.e. only the length of the bar is material and not the width, while in  two-dimensional histogram  both the length as well as the width are important.

The histogram is most widely used for the graphical presentation of a frequency distribution, however, we cannot construct a histogram for misleading if the distribution has unequal class-intervals and suitable adjustments in frequencies are not made.

The method of contracting histogram is given below (i) for distributions having equal class-intervals, and (ii) for distributions having unequal class-intervals.

Illustration: - represent the following data by a histogram:

Solution: As the class-intervals are unequal, the frequencies must be adjusted otherwise the histogram would give a misleading picture. The adjustment is completed as follows. The lowest class interval is 5. The frequencies of the class 30-40 are divided by 2. As the class interval is double, that of 40-60 by 4, etc.