Question

The frequency distribution for 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 = ${\displaystyle l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h}$

= ${\displaystyle 5+\left(\frac{80-45}{2\times 80-45-55}\right)\times 2}$

= ${\displaystyle 5+\left(\frac{35}{160-100}\right)\times 2}$

= ${\displaystyle 5+\frac{35\times 2}{60}}$

= 5 + 1.167

= 6.167

Hence, the modal agricultural holdings of the village is 6.167 hectares.