Question

Following table gives frequency distribution of milk (in litres) given per week by 50 cows.
Find average (mean) amount of milk given by a cow by 'shift of origin method'.

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

• A. $51.12$ litres
• B. $54.12$ litres
• C. $57.12$ litres
• D. $60.12$ litres

Answer 1

Answer: (C)

$57.12$ litres

Consider the following table, to calculate mean by "shift of origin method":

$x_i$=mid value of class interval

Assumed mean $a=57$

$ci$	$f_i$	$x_i$	$d_i=x_i-a$	$f_i{d}_i$
24-30	1	27	27-57= -30	-30
30-36	3	33	33-57= -24	-72
36-42	8	39	39-57= -18	-144
42-48	5	45	45-57= -12	-60
48-54	5	51	51-57= -6	-30
54-60	5	57	57-57=0	0
60-66	8	63	63-57=6	48
66-72	4	69	69-57=12	48
72-78	6	75	75-57=18	108
78-84	2	81	81-57=24	48
84-90	3	87	87-57=30	90

$N=\Sigma f_i=50$

$\Sigma f_i{d}_i=6$

Mean $\overline{x}=a+\frac{\Sigma f_i{d}_i}{N}$

$\therefore \overline{x}=57+\frac{6}{50}=57.12$

Average amount of milk given by cow is $57.12$ litres

Hence, option $C$ is correct.