During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight (in Kg) Less than (in kg) Less than 38

Question

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 1

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,

 \(\frac{N}{2}=\frac{35}{2}=17.5\)

The cumulative frequency is just greater than \(\frac{N}{2}\) 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 = I + \(\frac{\frac{N}{2}-C_1}{f}\times h\)

\(=46+\frac{17.5-14}{14}\times2\)

\(=46+\frac{7}{14}=46+0.5\)

= 46.5 kg

Hence, verified.