Question

The frequency distribution of weights of seeds is given. Draw both the types of ogive curves and find the median.

Weight (in mg)	11-20	21-30	31-40	41-50	51-60
No. of seeds	18	22	30	16	4

Answer 1

Here, the classes are to be made continuous. We find the less-than type cumulative frequencies by adding class frequencies from top to bottom and place them against the upper class boundaries.We take an additional point (lower boundary of the first class, 0)
Here, it is (10.5,0) (frequency 0) .We plot the points (u_i ,F_i ) and join the successive points by a free-hand curve .

We find the more-than type cumulative frequency by adding class frequencies from bottom to top and place it against the lower boundary of the class .We take an additional point (upper boundary of the last class, 0). Here, it is (60.5,0).

We plot the points (l_i , F_i' ) and join the successive points by a smooth free-hand curve .

The following table summarises the computations.

Classes	Extended classes	Frequencies	Upper class boundaries (ui )	Less-than cumulative frequencies (Fi )	Lower class boundaries (li )	More-than cumulative frequencies (Fi ')
-	-	-	10.5	0	-	-
11-20	10.5-20.5	18	20.5	18	10.5	90
21-30	20.5-30.5	22	30.5	40	20.5	86
31-40	30.5-40.5	30	40.5	70	30.5	70
41-50	40.5-50.5	16	50.5	86	40.5	40
51-60	50.5-60.5	4	60.5	90 = N	50.5	18
-	-	-		-	60.5	0

Both ogive curves are shown.


To find the median, draw a perpendicular AB to the X-axis from the point of intersection of the two curves .
The foot of perpendicular is the median. So, the median is 32 mg.