Question

A group of 10 observations has mean 5 and S.D. $2\sqrt{6}.$ Another group of 20 observations has mean 5 and S.D. $3\sqrt{2},$ then the S.D. of combined group of 30 observations is

• A. $\sqrt{5}$
• B. $2\sqrt{5}$
• C. $3\sqrt{5}$
• D. None of these

Answer 1

Answer: (B)

$2\sqrt{5}$

Here $n_1=10,{\overline{x}}_1=5,{\sigma }_1=2\sqrt{6}$
$n_2=20,{\overline{x}}_2=5,{\sigma }_2=3\sqrt{2}$
Now, $\sigma =\sqrt{\frac{n_1{\sigma }_1^2+n_2{\sigma }_2^2}{n_1+n_2}+\frac{n_1{n}_2}{n_1+n_2}{({\overline{x}}_1-x_2)}^2}$
$=\sqrt{\frac{10\times 24+20\times 18}{30}+0}$ $(\because {\overline{x}}_1={\overline{x}}_2)$
$=\sqrt{20}=2\sqrt{5}$