Question

Draw a cumulative frequency curve and cumulative frequency polygon for the following frequency distribution by less than method.

Age (in years)	0-9	10-19	20-29	30-39	40-49	50-59	60-69
No. of Persons:	5	15	20	23	17	11	9

Answer 1

The given frequency distribution is not continuous. So, we first make it continuous and prepare the cumulative frequency distribution as under.

Age (in years)	Frequency	Age less than	Cumulative frequency
-0.5-9.5	5	9.5	5
9.5-19.5	15	19.5	20
19.5-29.5	20	29.5	40
29.5-39.5	23	39.5	63
39.5-49.5	17	49.5	80
49.5-59.5	11	59.5	91
59.5-69.5	9	69.5	100

Now, we plot points $(9.5,5),\left(19.5\right),(29.5,40),(39.5,63),(49.5,80),(59.5,91)and(69.5,100)$. and join them by a free hand smooth curve to obtain the required ogive as shown in Fig. 7.5.
The cumulative frequency polygon is obtained by joining these points by line segments as shown in Fig. 7.6.