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

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Solution

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 = $L + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$
$= 4 + (\frac{80 - 70}{2 \times 80 - 70 - 60}) \times 1$
= 4 + 0.33
= 4.33
Hence, the modal fat content is 4.33 litres.

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Milk Sold (Litre)	1 - 2	2 - 3	3 - 4	4 - 5	5 - 6
No. of Customers	17	13	10	7	3

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

Milk(in litres)	24-30	30-36	36-42	42-48	48-54	54-60	60-66	66-72	72-78	78-84	84-90
No. of cows	1	3	8	5	5	5	8	4	6	2	3

Month	Jan	Feb	Mar	Apr	May	Jun
Milk (litres)	83	79	81	85	73	61

Yield per acre (quintal)	2 - 3	4 - 5	6 - 7	8 - 9	10 - 11
No. of farmers	30	50	55	40	20

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