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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 |
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
fo (frequency of the class preceding the modal class) = 20
f2 (frequency of the class succeeding the modal class) = 18
h (class size) = 2
Mode = \[L + \left( \frac{f_1 - f_0}{2 f_1 - f_0 - f_2} \right) \times h\]
\[= 9 + \left( \frac{35 - 20}{2 \times 35 - 20 - 18} \right) \times 2\]
= 9 + 0.9375
= 9.9375 ≈ 9.94
Hence, the mode of the supply of milk is 9.94 litres.
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