# The mean of five observations is M. If each observation is divided by 2,then what is the new set of observations?

$Letthesetofobservationsbe{x}_{1},{x}_{2},...,{x}_{n}.\phantom{\rule{0ex}{0ex}}Then,meanoftheseobservations=\frac{Sumofallobservations}{Numberofobservations}=\frac{{x}_{1}+{x}_{2}+...+{x}_{n}}{n}=M...\left(i\right)\phantom{\rule{0ex}{0ex}}Now,dividingeachobservationby2,thenewsetofobservationsis\frac{{x}_{1}}{2},\frac{{x}_{2}}{2},...,\frac{{x}_{n}}{2}.\phantom{\rule{0ex}{0ex}}Then,Sumofallnewobservations=\frac{{x}_{1}}{2}+\frac{{x}_{2}}{2}+...+\frac{{x}_{n}}{2}=\frac{1}{2}\left({x}_{1}+{x}_{2}+...+{x}_{n}\right)\phantom{\rule{0ex}{0ex}}Therefore,newmean=\frac{Sumofallnewobservations}{Numberofobservations}=\frac{\frac{1}{2}\left({x}_{1}+{x}_{2}+...+{x}_{n}\right)}{n}=\frac{1}{2}\times \frac{{x}_{1}+{x}_{2}+...+{x}_{n}}{n}=\frac{1}{2}M[From\left(i\right)]\phantom{\rule{0ex}{0ex}}NOTE:Since,thequestionisunclear,itisassumedintheabovesolutionthatthenewmeanisrequiredtobecalculated.$

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