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 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

⇒ Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

= `5 + ((80 - 45)/(2 xx 80 - 45 - 55)) xx 2`

= `5 + (35/(160 - 100)) xx 2`

= `5 + (35 xx 2)/60`

= 5 + 1.167

= 6.167

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