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.

Question

Philoid · Accepted Answer

Less than method:

It is given that on x-axis upper class limit and on y-axis cumulative frequency. We plot the points: (38,0); (40,3); (42,5); (49,9); (46,14); (48,28); (50,32); (52,35)

More than method:

Weight (in kg)	No. of students	More than	Cumulative frequency
38-40	3	38	35
40-42	2	40	32
42-44	4	42	30
44-46	5	44	26
46-48	14	46	21
48-50	4	48	7
50-52	3	50	3

X -axis lower class limit and y-axis cumulative frequency, we plot the points: (38,35); (40,32); (42,30); (44,26); (46,21); (48,7); (50,3)

We find the two types of cumulative frequency curves intersect at point P.

The value of M is 46.5 kg

Verification,

We have

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

Now, N = 35

Therefore, = = 17.5

The cumulative frequency is just greater than is 28 and the corresponding classes 46-48

Thus, 46-48 is the median class such that,

l = 46, f = 14, C₁ = 14 and h = 2

Median = l + * h

= 46 + * 2

= 46 + = 46 + 0.5

= 46.5 kg

Hence, verified.

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