This document discusses frequency polygons, which are a type of graphical representation of data that involves joining midpoints of histogram rectangles or data points with straight lines to form a polygon. Key details include: frequency polygons can be constructed from histograms or without histograms; they show the distribution of data by having point heights represent frequencies; and involve terms like class intervals, frequencies, midpoints, and class marks. Steps for drawing frequency polygons include constructing a histogram, marking midpoints, and joining points with straight lines. Advantages are that they help represent and compare data distributions clearly and simply. A disadvantage is they are less accurate than histograms since each class is represented by a single point.

1. FREQUENCY POLYGON
PRESENTED BY
MEENU M
2nd SEMESTER
B.Ed MATHEMATICS

2. GRAPHICAL REPRESENTATION OF DATA
 Data : Collection of facts or information
 It can be represented by a variety of graphs
 This gives a visual picture of the distribution
 Different types of Graphs
 Bar graph
 Pie graph
 Histogram
 Frequency polygon
 Frequency curve
 Ogives

3. FREQUENCY POLYGON
 It is a type of graphical representation of data
It is a line graph in which points are joined by straight lines to make a
polygon
 It can be constructed by joining the midpoints of the tops of all the
rectangles in a histogram
The height of the point represent the frequencies
It can also be drawn without constructing a Histogram

4. Terms associated with frequency polygon
 Class interval : Specific range in which data is going to
fall eg : 20-30
 Frequency : The number of times the observation
occurred
 Mid point : The center point of bar
 Upper limit (U.L) : Ending value of class interval
 Lower limit (L.L) : Starting value of class interval
 Class mark : Mid value of class
Class mark =
U.L+L.L
2

5. STEPS IN DRAWING A FREQUENCY POLYGON
1. Construct histogram
2. Mark midpoint
3. Join the points by straight line
4. Take rectangle of 0 heights and mark mid points
5. Join the the straight line to these newly marked points

6. Question :
Construct a frequency polygon using data given below:
MARKS 0 - 10 10 -20 20 - 30 30 - 40 40 - 50 50 - 60
No : of
students 5 10 15 20 15 5

7. 0 10 20 30 40 50 60
5
10
15
20
Marks
No
:
of
students
70
-10
Marks obtained by students

8. FREQUENCY POLYGON WITHOUT HISTOGRAM
Construct frequency polygon of following data:
MARKS 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90
No : of
students 5 10 15 20 15 5
Answer:
MARKS No : of Students Class mark
30 – 40 5 35 (
40+30
2
=
70
2
=35)
40 – 50 10 45
50 – 60 15 55
60 – 70 20 65
70 - 80 5 75

9. 30 40 50 60 70 80
5
10
15
20
MARK
No
of
students
Marks obtained by students
0

10. Advantages
It help to sort out and represent data
Give a clear picture distribution of data
Simple and easier to understand
We can draw two or more frequency polygons on the same axes/graph
 Thus we can make comparisons between the sets of data easily

11. Disadvantages
 Can be used only with continuous data
Less accurate representation of data because it represent
frequency of each class by single point
In short : It can mainly used to show the change and for comparison