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 agriculture holding per family. 

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

Mode = \(l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h\)

\(=5+\left(\frac{80-45}{2\times80-45-55}\right)\times2\)

\(=5+\frac{35}{60}\times2\)

\(=5+\frac{35}{30}\)

\(=6.2\)