Question

The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. Find the mode of fat content.

Content of fat (%)	2 - 3	3 - 4	4 - 5	5 - 6	6 - 7
Milk collected (Litre)	30	70	80	60	20

 

Answer 1

The maximum class frequency is 80.

The class corresponding to this frequency is 4 - 5.

So, the modal class is 4 - 5.

L (the lower limit of modal class) =  4

f₁ (frequency of the modal class) = 80 

f_o (frequency of the class preceding the modal class) = 70

f₂ (frequency of the class succeeding the modal class) = 60

h (class size) = 1 

Mode = \[L + \left(\frac{f_1 - f_0}{2 f_1 - f_0 - f_2} \right) \times h\]

= \[4 + \left(\frac{80 - 70}{2 \times 80 - 70 - 60} \right) \times 1\]

= 4 + 0.33

= 4.33

Hence, the modal fat content is 4.33.