A group of 10 observations has mean 5 and standard deviation $2 \sqrt{6} .$ Another group of 20 observation has mean 5 and standard deviation $3 \sqrt{2},$ then the standard deviation of combined group of 30 observationsis

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\sqrt{5}$

$3 \sqrt{5}$

$2 \sqrt{5}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$x_{1} = 5, σ_{1} = 2 \sqrt{6}, n_{1} = 10$
$x_{2} = 5 σ_{2} = 3 \sqrt{2}, n_{2} = 20$
combined variance $σ^{2} = \frac{n_{1} σ_{1}^{2} + n_{2} σ_{2}^{2}}{n_{1} + n_{2}} + \frac{n_{1} n_{2}}{{(n_{1} + n_{2})}^{2}} {({\bar{x}}_{1} - {\bar{x}}_{2})}^{2}$
$σ^{2} = \frac{(10) (24) + (20) (18)}{30} + \frac{200}{900} {(0)}^{2}$
$= \frac{240 + 360}{30} = \frac{600}{30} = 20$
$σ = \sqrt{20} = 2 \sqrt{5}$
standard deviation of combined group $= 2 \sqrt{5}$