# 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