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.

Given:

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

To do:

We have to draw a less than type ogive for the given data and obtain the median weight from the graph and verify the result by using the formula.

Solution:

We first prepare the cumulative  frequency distribution table by less than method as given below:

Represent weights along X-axis and cumulative frequency along Y-axis.

Plot the points (38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32), (52, 35) on the graph and join them in free hand to get an ogive as shown.

Here,

$N = 35$

$\frac{N}{2}=\frac{35}{2}=17.5$

From point $P$ (17.5) on Y-axis draw a line parallel to X-axis meeting the curve and then draw a line parallel to Y-axis meeting X-axis at $Q$.

From the figure, the median is 46.5 kg (approx.)

Therefore,
46-48 is the median class
Here,

$l= 46, h = 2,f= 14, F= 14$

This implies,

Median $=l+\frac{\frac{N}{2}-F}{f} \times h$

$=46+\frac{17.5-14}{14} \times 2$

$=46+\frac{3.5 \times 2}{14}$

$=46+0.5$

$=46.5$

Hence verified.