Graphical Representation

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

There are various methods of graphical representation of statistical data. In our study, we learn only two types.

(i) Histogram

(ii) Ogive or Cumulative Frequency Curve

Histogram

A histogram is a diagram which represents the class interval and the frequency in the form of a rectangle. There will be as many adjoining rectangles as there are class intervals.

The class limits are marked on the horizontal axis.

The frequency is marked on the vertical axis.

Thus a rectangle is constructed on each class interval.

If the intervals are equal, then the height of each rectangle is proportional to the corresponding class frequency.

If the intervals are unequal, then the area of each rectangle is proportional to the corresponding class frequency.

In the above example, the intervals are exclusive.

Now, let us consider an example with inclusive intervals.

The daily wages of 50 workers, in dollars, are given below:

Table (a)

In table (a), the class intervals are inclusive. So, we convert them to the exclusive form as shown in table (b)

Table (b)

(i) The class intervals are made continuous and then the histogram is constructed.

(ii) A kink or a zig-zag curve is shown near the origin. It indicates that the scale along the horizontal axis does not start at the origin.

(iii) The horizontal scale and the vertical scale need not be same.

Distribution of shops according to the number of wage-earners employed at a shopping complex is given below:

Illustrate the above table by a histogram, showing clearly how you deal with the unequal class intervals.

When the intervals are unequal, we construct each rectangle with the class interval as the base and frequency density as the height.

Frequency density

In the above example, take second class interval,

its frequency density

Similarly for the last interval,

the frequency density