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.

Age (years)	Less than 5	5 - 9	10 - 14	15 - 19	20 - 24	25 - 29
No. of patients	38	32	50	36	24	20

Answer 1

Converting the given table into continuous class, we get

Age (years)	0.5 - 4.5	4.5 - 9.5	9.5 - 14.5	14.5 - 19.5	19.5 - 24.5	24.5 - 29.5
No. of patients	38	32	50	36	24	20

The maximum class frequency is 50.
The class corresponding to this frequency is 9.5 - 14.5.
So, the modal class is 9.5 - 14.5.
L (the lower limit of modal class) = 9.5
f₁ (frequency of the modal class) = 50
f_o (frequency of the class preceding the modal class) = 32
f₂ (frequency of the class succeeding the modal class) = 36
h (class size) = 5
Mode = $L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$
$=9.5+\left(\frac{50-32}{2\times 50-32-36}\right)\times 5$
= 9.5 + 2.81
= 12.31
Hence, the modal age is 12.31 years.