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

Answer

The mode of the supply of milk is ` 9.94` litres.

Explanation

Here, the maximum frequency (35) is in the class `9 - 11` .
` :. ` the modal class is `9 - 11` .
In the given example,
L = Lower class limit of the modal class = 9
h = Class interval of the modal class = 2
`f_(1)` = Frequency of the modal class = 35
` f_(0)` = Frequency of the , class preceding the modal class = 20
` f_(2)` = Frequency of the class succeeding the modal class = 18
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 approx 9.94`