5. Following table gives frequency distribution of milk (in litres) given per week by 50 cows.
| 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 |
Find average (mean) amount of milk given by a cow by 'shift of origin method'.
Solution:
Class width ($h$) = 6, Assumed mean ($A$) = 57
Milk
(in litres)Class Mark
($x_i$)$d_i = x_i - A$ No. of cows
($f_i$)$f_i d_i$ 24 - 30 27 -30 1 -30 30 - 36 33 -24 3 -72 36 - 42 39 -18 8 -144 42 - 48 45 -12 5 -60 48 - 54 51 -6 5 -30 54 - 60 57 → A 0 5 0 60 - 66 63 6 8 48 66 - 72 69 12 4 48 72 - 78 75 18 6 108 78 - 84 81 24 2 48 84 - 90 87 30 3 90 Total 50 6 $$ \begin{align*} \bar{d} &= \frac{\sum f_i d_i}{\sum f_i} \\ \therefore \bar{d} &= \frac{6}{50} \\ \therefore \bar{d} &= 0.12 \\ \text{Mean } (\bar{x}) &= A + \bar{d} \\ &= 57 + 0.12 \\ &= 57.12 \end{align*} $$