Question

Draw both ogive curves on the same graph paper for the following frequency distribution. Also find the median.

Intelligence quotient (IQ)	60-79	80-99	100-119	120-139	140-159	Total
Number of students	2	9	15	11	3	40

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 it against the upper class boundary .We take an additional point (lower boundary of the first class, 0).
Here, it is (59.5,0) (frequency zero).We plot the points (u_i ,F_i ) and join 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 (159.5,0).

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 ')
-	-	-	59.5	0	-	-
60-79	59.5-79.5	2	79.5	2	59.5	40
80-99	79.5-99.5	9	99.5	11	79.5	37
100-119	99.5-119.5	15	119.5	26	99.5	26
120-139	119.5-139.5	11	139.5	37	119.5	11
140-159	139.5-159.5	3	159.5	40=N	139.5	2
-	-	-		-		0

The ogive curves are shown below.



From the graph, we find that the value of median is 111 IQ.