The frequency distribution table of agricultural 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 agricultural holdings of the village
Solution:
Given, the above data represents the frequency distribution of agricultural holdings in a village.
We have to find the modal agricultural holdings of the village.
| Area of land (in hectares) | Number of families |
| 1 - 3 | 20 |
| 3 - 5 | 45 |
| 5 - 7 | 80 |
| 7 - 9 | 55 |
| 9 - 11 | 40 |
| 11 - 13 | 12 |
Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]h
Where, l is the lower limit of the modal class
f₁ is the frequency of the modal class
f₀ is the frequency preceding the modal class
f₂ is the frequency succeeding the modal class
h is the class size
From the table,
Maximum frequency = 80
This frequency lies in the class 5-7
l = 5
h = 2
f₁ = 80
f₀ = 45
f₂ = 55
Now, f₁ - f₀ = 80 - 45 = 35
2f₁ - f₀ - f₂ = 2(80) - 45 - 55
= 160 - 100
= 60
[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 35/60
= 7/12
Now, mode = 5 + (7/12)2
= 5 + (14/12)
= 5 + 7/6
= 5 + 1.17
= 6.17
= 6.2
Therefore, the mode of the given data is 6.2
✦ Try This: The frequency distribution table of agricultural 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 | 25 | 49 | 90 | 85 | 60 | 32 |
Find the modal agricultural holdings of the village.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14
NCERT Exemplar Class 10 Maths Exercise 13.3 Sample Problem 4
The frequency distribution table of agricultural 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 agricultural holdings of the village
Summary:
The modal agricultural holdings of the village is 6.2 hectares
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