3. The measurements (in mm) of the diameters of the head of screws are given below :
| Diameter (in mm) | 33 - 35 | 36 - 38 | 39 - 41 | 42 - 44 | 45 - 47 |
|---|---|---|---|---|---|
| No. of screws | 10 | 19 | 23 | 21 | 27 |
Calculate mean diameter of head of a screw of 'Assumed Mean Method'.
Solution:
Class width ($h$) = $3$, Assumed mean ($A$) = $40$
Diameter
(in mm)Class Mark
($x_i$)$d_i = x_i - A$ No. of screws
($f_i$)$f_i d_i$ 33 - 35 34 $-6$ 10 $-60$ 36 - 38 37 $-3$ 19 $-57$ 39 - 41 40 $\leftarrow A$ $0$ 23 $0$ 42 - 44 43 $3$ 21 $63$ 45 - 47 46 $6$ 27 $162$ Total 100 108 $$\bar{d} = \frac{\sum f_i d_i}{\sum f_i}$$
$$\therefore \bar{d} = \frac{108}{100}$$
$$\therefore \bar{d} = 1.08$$
$$\text{Mean } (\bar{x}) = A + \bar{d}$$
$$= 40 + 1.08$$
$$= 41.08$$