Question

Draw a cumulative frequency curve (less than type) for the following data and find the median from it:

Class interval	200-220	220-240	240-260	260-280	280-300	300-320
Frequency	7	3	6	8	2	4

Answer 1

From the given table, we may prepare the 'less than' frequency table as shown below:

Class	c.f
Less than 220	7
Less than 240	10
Less than 260	16
Less than 280	24
Less than 300	26
Less than 320	30

We plot the points A(220,7), B(240,10), C(260,16), D(300,24), E(300,26) and F(320,30).
Join AB, BC, CD, DE, EF and FA with a free hand to get the curve representing the ‘less than type’ series.


Here, N=30
$\Rightarrow$$\frac{N}{2}=15$
From P(0,15), draw $PQ$$\parallel x-\mathrm{axis}$ meeting the curve at Q. Draw $QM$$\perp OX$ meeting $x-\mathrm{axis}$ at M.
Clearly, OM= 256 units
Hence, Median=256