Question

Draw frequency polygons for each of the following frequency distribution:
(a) using histogram
(b) without using histogram

C.I	5 -15	15 -25	25 -35	35 - 45	45-55	55-65
ƒ	8	16	18	14	8	2

Answer 1

Using Histogram:

C.I.	f
5 - 15	8
15 - 25	16
25 - 35	18
35 - 45	14
45 - 55	8
55 - 65	2

Steps:

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.
2.  
3. On a graph paper, mark class-marks along X-axis and frequencies along Y-axis.
4. On this graph paper, mark points taking values of class-marks along the X-axis and the values of their corresponding frequencies along the Y-axis.
5.  
6. Draw line segments joining the consecutive points marked in step (3) above.
   

   C.I.	Class-mark	f
   -5 - 5	0	0
   5 - 15	10	8
   15 - 25	20	16
   25 - 35	30	18
   35 - 45	40	14
   45 - 55	50	8
   55 - 65	60	2
   65 - 75	70	0