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

From the given data, to represent the table in the form of graph, choose the upper limits of the class intervals are in x-axis and frequencies on y-axis by choosing the convenient scale.

Now plot the points corresponding to the ordered pairs given by (38, 0), (40, 3), (42, 5), (44, 9),(46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper an join them to get a smooth curve. The curve obtained is known as less than type ogive.



Locate the point 17.5 on the y-axis and draw a line parallel to the x-axis cutting the curve at a point. From the point, draw a perpendicular line to the x-axis. The intersection point perpendicular to x-axis is the median of the given data. Now, to find the mode by making a table.

The class 46-48 has the maximum frequency, therefore, this is modal class

Here, l = 46, h = 2, f₁ = 14, f₀ = 5 and f₂ = 4

Now, Mode \( = \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)

\(= \ 46 \ + \ \frac{14 \ - \ 5}{28 \ - \ 5 \ - \ 4} \ × \ 2 \ \)

\( = \ 46 \ + \ \frac{9}{19} \ × \ 2 \)

\(= \ 46 \ + \ 0.95 \ = \ 46.95 \)

Thus, mode is verified.