The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares):	1-3	3-5	5-7	7-9	9-11	11-13
Number of families:	20	45	80	55	40	12

Find the modal agriculture holdings of the village.

Given:

The frequency distribution table of agriculture holdings in a village is given.

To do:

We have to find the modal agriculture holdings of the village.

Solution:

The frequency of the given data is as given below.

Area of land (in hectares)($x_i$):	Number of families$(f_i$):
1-3	20
3-5	45
5-7	80
7-9	55
9-11	40
11-13	12

We observe that the class interval of 5-7 has the maximum frequency(80).

Therefore, it is the modal class.

Here,

$l=5, h=2, f=80, f_1=45, f_2=55$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=5+\frac{80-45}{2 \times 80-45-55} \times 2$

$=5+\frac{35}{160-100} \times2$

$=5+\frac{70}{60}$

$=5+1.16$

$=6.16$

The modal agriculture holdings of the village is 6.2 hectares.