Question

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 agricultural holdings of the village .

Answer 1

The maximum class frequency is 80. The class corresponding to this frequency is 5–7.
So, the modal class is 5–7.
l (the lower limit of modal class) = 5
f₁ (frequency of the modal class) = 80
f₀ (frequency of the class preceding the modal class) = 45
f₂ (frequency of the class succeeding the modal class) = 55
h (class size) = 2
$$\begin{gathered} \mathrm{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h \\ =5+\left(\frac{80-45}{2\times 80-45-55}\right)\times 2 \\ =5+\frac{35}{60}\times 2 \\ =5+\frac{35}{30} \\ =6.2 \end{gathered}$$

Hence, the modal agricultural holdings of the village is 6.2 hectares.