Two sets each of 20 observations have the same standard derivation 5. The first set has a mean 17 and second a mean 22. Then the standard deviation of the set obtained by combining the given two sets.

Answer

N/a

Explanation

Given `n_(1)=20,sigma_(1)=5,barx_(1)=17 and n_(2)=20 ,sigma_(2)=5 ,barx_(2)=22`
We know that `sigma=sqrt((n_(1)s_(1)^(2)+n_(2)s_(2)^(2))/(n_(1)+n_(2))+(n_(1)n_(2)(barx_(1)-barx_(2))^(2))/((n_(1)+n_(2))^(2)`
`=sqrt((20xx(5)^2+20xx(5)^2)/(20+20)+(20xx20(17-22)^(2))/((20+20)^(2)))`
`=sqrt(1000/40+(400 xx25)/1600)=sqrt(25+25/4)=sqrt(125/4)=sqrt(31.25)=5.59`