How do you draw frequency polygon?
The following steps will be useful to draw frequency polygon without histogram.Step 1 :Obtain the frequency distribution and compute the mid points of each class interval.Step 2 :R
The following steps will be useful to draw frequency polygon without histogram.
Step 1 :
Obtain the frequency distribution and compute the mid points of each class interval.
Step 2 :
Represent the mid points along the X-axis and the frequencies along the Y-axis.
Step 3 :
Plot the points corresponding to the frequency at each mid point.
Step 4 :
Join these points, by straight lines in order.
Step 5 :
To complete the polygon join the point at each end immediately to the lower or higher class marks (as the case may be at zero frequency) on the X-axis.
Example 1 :
Draw a frequency polygon for the following data without using histogram.
Class interval
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
80 - 90
Frequency
4
6
8
10
12
14
7
5
Solution :
Class interval
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
80 - 90
90 - 100
Mid points
5
15
25
35
45
55
65
75
85
95
Frequency
0
4
6
8
10
12
14
7
5
0
Mark the class intervals along the X-axis and the frequency along the Y-axis. We take the imagined classes 0-10 at the beginning and 90-100 at the end, each with frequency zero. We have tabulated the data as shown.
Using the adjacent table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).
We draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ to obtain the required frequency polygon ABCDEFGHIJ, which is shown in the picture given below.
Scale :
X - axis 1 cm = 10 units
Y - axis 1 cm = 2 units
Example 2 :
Draw a frequency polygon for the following data without using histogram
Age (in years)
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
Number of persons
6
11
25
35
18
12
6
Solution :
Class interval
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
Mid points
5
15
25
35
45
55
65
75
Frequency
6
11
25
35
18
12
6
0
Mark the class intervals along the X-axis and the frequency along the Y-axis. We take the imagined classes 0-10 at the beginning and 60-70 at the end, each with frequency zero. We have tabulated the data as shown.
Using the adjacent table, plot the points A (5, 6), B (15, 11), C (25, 25), D (35, 35), E (45, 18), F (55, 12), G (65, 6), and H (75, 0)
We draw the line segments AB, BC, CD, DE, EF, FG, GH, HI to obtain the required frequency polygon ABCDEFGHI, which is shown in the picture given below.
Scale :
X - axis 1 cm = 10 units
Y - axis 1 cm = 5 units
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