Question

Find combined mean and S.D.

	A	B
No. of workers	$100$	$200$
Mean salary	$1600$	$1800$
S.D.	$16$	$18$

• A. $1800,96$
• B. $95.87,1733$
• C. $1733.3,95.84$
• D. $1600,85.25$

Answer 1

The correct option is C $1733.3,95.84$

$n_1=100,{\overline{x}}_1=1600,{\sigma }_1=16,$ $n_2=200,{\overline{x}}_2=1800,{\sigma }_2=18$

$\overline{x}=\frac{n_1{\overline{x}}_1+n_2{\overline{x}}_2}{n_1+n_2}=\frac{100\times 1600+200\times 1800}{300}=1733.3$ $Rs.$

$d_1={\overline{x}}_1-\overline{x}=1600-1733.3=-133.3$

$d_2={\overline{x}}_2-\overline{x}=1800-1733.3=66.7$

${\sigma }^2(n_1+n_2)=n_1({\sigma }_1^2+d_1^2)+n_2({\sigma }_2^2+d_2^2)$

${\sigma }^2\left(800\right)=100\times (256+17768.89)+200(324+4443.55)$

${\sigma }^2=9186.66$

$\sigma =95.84$