Question

The measurements(in mm) of the diameters of the heads 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 the mean diameter by the assumed-mean method.

Answer 1

Diameter(in mm) (Class interval)	Class Marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-40 \end{gathered}$$	No. of screws $\left(f_i\right)$	$\left(f_i\right)\left(d_i\right)$
33-35	34	$-$6	10	$-$60
36-38	37	$-$3	19	$-$57
39-41	$40\to A$	0	23	0
42-44	43	3	21	63
45-47	46	6	27	162
Total	-	-	$\sum _{}^{}{f}_i=100$	$\sum _{}^{}{f}_i{d}_i=108$

$$\begin{gathered} \overline{d}=\frac{{\displaystyle \sum _{}^{}}{f}_i{d}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{108}{100}=1.08 \\ \mathrm{Mean}=\overline{x}=A+\overline{d}=40+1.08=41.08 \end{gathered}$$

∴ Mean diameter is 41.08 mm.