Question

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 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52	0 3 5 9 14 28 32 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.

Answer 1

Prepare the table for cumulative frequency for less than type.

Weight (in kg)	No. of students	Weight (less than)	Cumulative frequency	Suitable points
36–38	0	38	0	(38, 0)
38–40	3	40	3	(40, 3)
40–42	2	42	5	(42, 5)
42–44	4	44	9	(44, 9)
44–46	5	46	14	(46, 14)
46–48	14	48	28	(48, 28)
48–50	4	50	32	(50, 32)
50–52	3	52	35	(52, 35)

Now, draw the less than ogive using suitable points.

Here, =

From (0, 17.5) draw a line parallel to horizontal axis, which intersects the graph at the point M having x-coordinate as 46.5.

Therefore, the median is 46.5 kg.

Calculation for median using formula.

Now,

So, 46–48 is the median class.

Here,

Hence, both the methods give same result.