Frequency polygon

Frequency polygon is another way to show the information in a frequency table. It looks a little bit like a line graph. To make a frequency-polygon, you just need to plot a few points and then join the points by straight lines.
Frequency-polygon of a given frequency distribution can be drawn in two ways.
1) By using histogram 2) Without using histogram
After drawing a histogram, obtain the midpoints of each class. The midpoint of a class is the point in the middle of the class. So for instance, if I have a class “10 – 19", then the midpoint is ( 10+19)/2 = 14.5. A class of “0 – 5" has a midpoint of 2.5. Join these mid points of the adjacent rectangles of the histogram by dotted line segments. Obtain the mid points of two class intervals of zero frequency on X-axis, one adjacent to the first, on its left and one adjacent to the last, on its right. These class-intervals are known as imagined class intervals.

Note : Sometimes imagined class intervals do not exist. For example marks obtained by the students in a test, we can not go below zero and beyond maximum marks on the two sides. In such cases extreme line-segments are partly drawn and are brought down vertically so that they meet with the vertical sides of first and the last rectangles.

Example without using histogram :

Age in years	Class marks	Frequency
0 - 2	1	2
2 - 4	3	4
4 - 6	5	6
6 - 8	7	8
8 -10	9	9
10- 12	11	6
12-14	13	5
14- 16	15	3
16- 18	17	1

Note: Class marks are obtained by adding the age in years and divide it by 2.

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