Question

Draw frequency polygons for each of the following frequency distribution: 

(a) using histogram

(b) without using histogram

C.I	10 - 30	30 - 50	50 - 70	70 - 90	90 - 110	110 - 130	130 - 150
ƒ	4	7	5	9	5	6	4

Answer 1

using histogram

C.I	ƒ
10 - 30	4
30 - 50	7
50 - 70	5
70 - 90	9
90 - 110	5
110 - 130	6
130 - 150	4

Steps:

1. 1. Draw a histogram for the given data.
   2. Mark the mid-point at the top of each rectangle of the histogram drawn.
   3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
   4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon. 

Without using Histogram:

Steps: 

1. Find the class-mark (mid-value) of each given class-interval.
   classmark = mid-value = ${\displaystyle \frac{\text{Upper limit + Lower limit}}{2}}$
2. On a graph paper, mark class-marks along X-axis and frequencies along Y-axis.

3. On this graph paper, mark points taking values of class-marks along the X-axis and the values of their corresponding frequencies along Y-axis.

4. Draw line segments joining the consecutive points marked in step (3) above.

   C.I.	Class-mark	f
   -10 - 10	0	0
   10 - 30	20	4
   30 - 50	40	7
   50 - 70	60	5
   70 - 90	80	9
   90 - 110	100	5
   110 - 130	120	6
   130 - 150	140	4
   150 - 170	160	0

5.