During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight (in kg) Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Let us now plot the points corresponding to the ordered pairs given by (38,0),(40,3),(42,5),(44,9),(46,14),(48,28),(50,32) and (52,35) on a graph paper and join them by a free hand smooth curve.

Now,
Weight (in kg) Number of students (Frequency)
0-38 0
38-40 3
40-42 2
42-44 4
44-46 5
46-48 14
48-50 4
50-52 3

Mode: The class which have highest frequency. In this case, class interval 46-48 is the modal class.

Now, Lower limit of modal class, l=46, h=2, f1=14, f0=5, f2=4

We know that,
Mode = l + ((f1-f0)/(2f1-f0-f2)) * h
= 46 + ((14-5)/(2(14)-5-4)) * 2
= 46 + (9/19) * 2
= 46 + 0.95
Mode = 46.95, verified.