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The mean and standard deviation deviatio...

The mean and standard deviation deviation of some data for the time taken to complete a test are calculated with the following results
Number of observation =25,means=18.2 s,standard deviation =3.25 s further another set of 15 obserbvation `x_(1),x_(2)...x_(15)` also in seconds is now available and we have `Sigma_(i=1)^(15) x_(i)=279 and Sigma_(i =1)^(15) x_(i)^(2)=5524 ` .Calculate the standard derivation based on all 40 observation .

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Given `n_(i)=25,barx_(i)=18.2,sigma_(1)=3.25,`
`n_(2)=15 overset(15)underset(i=1)Sigma x_(i)=279 and overset(15)underset(i=1)Sigma x_(i)^(2)=5524 `
For first set `Sigmax_(i)=25xx18.2=455`
`therefore sigma_(1)^(2)=Sigma=(Sigma x_(i)^(2))/25-(18.2)^(2)`
`rArr (3.25)^(2)=Sigmax_(i)^(2)/25-33.1 24 `
`rArr 10.5625+331.24=(Sigmax_(i)^(2))/(25)`
`rArr Sigmax_(i)^(2)=25xx(10.5625+331.24)=25xx341.8025`
8545.0625
For combined SD of the 40 observations n=40
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