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

Using histogram

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 midpoints of the upper horizontal size of each rectangle.
(iii) Obtain the midpoint 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 midpoints of the adjacent rectangles of the histogram by dotted line segment.
(v) Complete the polygon by joining the midpoints of the first and last class intervals to the midpoints of zero frequency class intervals.
The monthly earnings of 30 employees are given below:
Monthly income (Rs) 
15001600 
16001700 
17001800 
18001900 
19002000 
No. of employees 
3 
5 
10 
8 
4 
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 (midpoints) of each class interval.
3. Choose a suitable scale and represent the class marks on the xaxis.
4. Choose a suitable scale for frequencies and mark them on the yaxis 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 midpoints of the imagined classes adjacent to them.
Draw the frequency polygon without using histogram for the followings:
Cost of living index 
440460 
460480 
480500 
500520 
520540 
540560 
560580 
580600 
No of months 
2 
4 
3 
5 
4 
3 
1 
2 