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

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Solution

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
f_o (frequency of the class preceding the modal class) = 20
f₂ (frequency of the class succeeding the modal class) = 18
h (class size) = 2
Mode = $L + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$
$= 9 + (\frac{35 - 20}{2 \times 35 - 20 - 18}) \times 2$
= 9 + 0.94
= 9.94
Hence, the the mode of the supply of milk is 9.94 litres.

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