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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 |
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.
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