If the mean and standard deviation of 75 observations is 40 and 8 respectively, find the new mean and standard deviation if
(i) each observation is multiplied by 5.
(ii) 7 is added to each observation.

Explanation

Given: `barX=40,sigma=8, N=75`
(i) A "change of scale" affects the value of both `barX` and `sigma`. A change of scale occurs when each observation is multiplied by a constant. As a result to that, `barX` and `sigma` also get multiplied by that constant.
Hence,
New `barX="Old "barXxx5`
`=40xx5`
=200
and,
New `sigma="Old "sigmaxx5`
`=8xx5`
=40
(ii) A "change of origin " affects the value of `barX` but not that of `sigma`. A change of origin occurs when eachobservation is increased by a constant .As a result to that, `barX` also increases by the same constant, while `sigma` remains unchanged.
In our question, that constant is 7.
Hence,
New`barX="Old "barX+7`
`=40+7`
=47
While,
New `sigma="Old "sigma`
=8