Question

The means of two samples of sizes 10 and 20 are 24 and 45 respectively and the standard deviations are 6 and 11. Obtain the standard deviation of the sample of the sample of size 30 obtained by combining the two samples.

Answer 1

Answer:

composed mean = 38 composed S D = 13.80

Answer 2

Answer:

Standard Deviation of the sample of size 30 is equal to 13.80 by combining two samples.

Step-by-step explanation:

• Given that

                       $n_{1} =10, \\ n_{2} = 20,$   $x_{1} =24,\\ x_{2}=45,$  $\sigma_{1}=6\\ \sigma_{2} =11$

•    Combined mean   $(x)=\frac{n_{1}\bar x_{1}+ n_{2} \bar x_{2}}{n_{1} +n_{2} }$

                                   $x=\frac{(10)(24)+(20)(45)}{10+20} =\frac{1140}{30}$

                                   $x=38$

•              $d_{1} =\bar x_{1} -\bar x =24-38=-14\\ d_{2} =\bar x_{2} -\bar x=45-38=7$

•   Combined Standard deviation,

                               $d=\sqrt\frac{{n_{1}(\sigma_{1}^{2}+d_{1}^{2} ) +n_{2} (\sigma_{2}^{2}+d_{2}^{2} ) }}{n_{1} +n_{2} }$

                   ∴           $d=\sqrt\frac{10(196+36)+20(49+121)}{10+20} \\ d=\sqrt\frac{5720}{30} \\ d=\sqrt{190.66}\\ d=13.80$

    Therefore, the standard deviation is 13.80 obtained by combining the two samples.