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 a free hand to get an ogive as shown.
Here,
$N = 35$
$\frac{N}{2}=\frac{35}{2}=17.5$
From the point, $P$ (17.5) on Y-axis draw a line parallel to X-axis meeting the curve and then draw a line parallel to the Y-axis meeting the 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.
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