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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. |
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Answer» 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 |
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