Question

	A	B
No. of workers	$500$	$600$
Mean	$200$	$300$
S.D.	$9$	$10$

Find combined mean and S.D.

• A. $254.54,50.70$
• B. $25.5,51$
• C. $257.23,52.5$
• D. $250,9.5$

Answer 1

The correct option is A $254.54,50.70$

$n_1=500,{\overline{x}}_1=200,{\sigma }_1=9,$ $n_2=600,{\overline{x}}_2=300,{\sigma }_2=10$

$\overline{x}=\frac{n_1{\overline{x}}_1+n_2{\overline{x}}_2}{n_1+n_2}=\frac{500\times 200+600\times 300}{1100}=254.545$

$d_1={\overline{x}}_1-\overline{x}=200-254.545=-54.545$

$d_2={\overline{x}}_2-\overline{x}=300-254.545=45.455$

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

${\sigma }^2\left(1100\right)=500\times (81+2975.15)+600(100+2066.157)$

${\sigma }^2=2570.699$

$\sigma =50.7$