Question

From the following frequency distribution, prepare the 'Less Than Ogive'.

Capital (in Lak of Rs)	Number of Companies
0-10	2
10-20	3
20-30	7
30-40	11
40-50	15
50-60	7
60-70	2
70-80	3

Also, Find the median.

Answer 1

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

Capital (in Lakhs)	Number of companies
Less than 10	2
Less than 20	5
Less than 30	12
Less than 40	23
Less than 50	38
Less than 60	45
Less than 70	47
Less than 80	50

We plot the points A(10,2), B(20,5), C(30,12), D(40,23), E(50,38), F(60,45), G(70,47) and H(80,50).
Join AB, BC, CD, DE, EF, FG, GH and HA with a free hand to get the curve representing the ‘less than type’ series.


Here, N=50
$\Rightarrow \frac{N}{2}=25$
From P(0,25), draw PQ meeting the curve at Q. Draw QM meeting at M.
Clearly, OM = Rs 42 Lakh
Hence, median = Rs 42 Lakh