Question

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

Milk (Litre)	1-3	3-5	5-7	7-9	9-11	11-13
No. of hotels	7	5	15	20	35	18

Answer 1

Milk (Litre)	1-3	3-5	5-7	7-9	9-11	11-13
No. of hotels	7	5	15	20 → f0	35 → f1	18 → f2

The maximum class frequency is 35.

The class corresponding to this frequency is 9-11.

So, the modal class is 9-11. 

L (the lower limit of modal class) =  9

f₁ (frequency of the modal class) = 35 

f₀ (frequency of the class preceding the modal class) = 20

f₂ (frequency of the class succeeding the modal class) = 18

h (class size) = 2

Mode = `L + [(f_1 - f_0)/(2f_1 - f_0 - f_2)] xx h`

= `9 + [(35 - 20)/(2 xx 35 - 20 - 18)] xx 2`

= `9 + (15/(70 - 38)) xx 2`

= `9 + 15/32 xx 2`

= `9 + 15/16`

= 9 + 0.9375

= 9.9375 ≈ 9.94

Hence, the mode of the supply of milk is 9.94 litres.