# Introduction for Frequency Polygon

Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are helpful in comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions.

Frequency polygon can be drawn in two different ways

1. Using histogram

2. Without using histogram

In order to draw the frequency polygon we may follow the following steps:

# Frequency Polygon using Histogram

(i) Obtain the frequency distribution and construct the histogram representing it.

(ii) Obtain the mid-points of the upper horizontal size of each rectangle.

(iii) Obtain the mid-point of two class intervals of zero frequency, one on the left side of first rectangle and the other on the right side of the last rectangle.

(iv) Join these mid-points of the adjacent rectangles of the histogram by dotted line segment.

(v) Complete the polygon by joining the mid-points of the first and last class intervals to the mid-points of zero frequency class intervals.

Example

The monthly earnings of 30 employees are given below:

 Monthly income (Rs) 1500-1600 1600-1700 1700-1800 1800-1900 1900-2000 No. of employees 3 5 10 8 4

Solution

Draw the histogram and frequency polygon for the above data.

The frequency polygon is shown by the dotted line.

# Frequency without Polygon using Histogram

To draw a frequency polygon without using the histogram follow the steps given below:

Procedure :-
1. Obtain the given frequency distribution.

2. Obtain the class marks (mid-points) of each class interval.

3. Choose a suitable scale and represent the class marks on the x-axis.

4. Choose a suitable scale for frequencies and mark them on the y-axis above the class marks.

5. Join the point by line segments.

6. Complete the frequency polygon by joining the class marks of the first and last class intervals to the mid-points of the imagined classes adjacent to them.

Example

Draw the frequency polygon without using histogram for the followings:

 Cost of living index 440-460 460-480 480-500 500-520 520-540 540-560 560-580 580-600 No of months 2 4 3 5 4 3 1 2

Solution