Q. 94.7( 11 Votes )

During the medical check-up of 35 students of a class, their weights were recorded as follows:


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 :

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:



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



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.


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