FSeries = {63.2,70.1,74.2,76.1,77.4,78.4}
SSeries = {63,68.7,74,76,77.5,83.7}
TSeries  = {63,69.5,74,75.8,77.4,83.7}

AvgMes = Table[ (FSeries[[i]] + SSeries[[i]] + TSeries[[i]])/3,{i,6}]
InfMesAvg = 83.7

YAxes =Map[Function[x ,0.01Abs[(x - InfMesAvg )]],AvgMes]

XAxes = {1/2,1/3,1/4,1/5,1/6,1/7}

Args = Table[{XAxes[[i]],YAxes[[i]]},{i,6}]
f = LinearModelFit[Args,{1,x},x]
Show[Plot[f[x],{x,0,1}],ListPlot[Args]]

Fact = f'[x]

(10^-3*0.5)^2 / Fact

KError = f["EstimatedVariance"]
RError = 0.02*10^-3

IError = Sqrt[(10^-3*RError/Fact)^2 + (KError*(0.5*10^-3)^2/Fact^2)^2]/4