Question

The measurement in mm) of the diameters of the head of screws are give below:
Diameter (in mm
No of screws
33 - 35
10
36 - 38 | 39 - 41
19 23
42-44
21
45-47
22
Calculate mean by Assumed mean method.
Sol.
Diameter (in mm)
class mark (xi)
di = xi-A
di = ._-
No of screws
fidi
60
33 - 35
36-38
39 - 41
42 - 44
45-47
34
37
40
91700
46
03
Efidi =
T-Ifidi -
Mean (1)=A+
,​

Answer 1

Answer:

1 Answer

Consider the following table, to calculate mean:

$$ci$$ $$f_i$$ $$x_i$$ $$f_ix_i$$

32.5-35.5 10 34 340

35.5-38.5 19 37 703

38.5-41.5 23 40 920

41.5-44.5 21 43 903

44.5-47.5 27 46 1242

$$N=\Sigma f_i=100$$

$$\Sigma f_ix_i=4108$$

Mean $$\overline x=\dfrac {\Sigma f_ix_i}{N}$$

$$\therefore \overline x=\dfrac{4108}{100}=41.08$$

Mean diameter of head of a screw is $$41.08$$mm

Hence, option $$C$$ is correct.