Draw frequency polygons for 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
f	4	7	5	9	5	6	4

(a) Using histogram

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 (in the given question, the immediately lower class-interval is -10 - 10) and mid-point of the immediately higher class-interval (in the given question the immediate upper class-interval is 150 - 170).

4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

(b) Without using histogram

Steps:

1. Find the class-mark (mid-value) of each given class-interval.

   Class-mark = mid-value = $\dfrac{\text{Upper limit + Lower limit}}{2}$

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 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.