(*#6*)
ApertureMeas6 = {{4.8,5.26},{5.78,6.21},{5.23,5.83}};
(*#14*)
ApertureMeas14 = {{5.64,6.38},{5.84,6.55},{6.34,6.92}};

DeltaApertyre6 = Function[x, {(x[[2]]  - x[[1]]) * 10^(-6)}]/@ ApertureMeas6
DeltaApertyre14 = Function[x, {(x[[2]]  - x[[1]]) * 10^(-6)}]/@ ApertureMeas14
TotalOfApertyre6 = 10^(-4)*Total[Map[Function[x,x[[2]] - x[[1]]],ApertureMeas6,{1}]]/3
TotalOfApertyre14=  10^(-4)*Total[Map[Function[x,x[[2]] - x[[1]]],ApertureMeas14,{1}]]/3

Error6 = DeltaApertyre6- TotalOfApertyre6
Error14 = DeltaApertyre14 - TotalOfApertyre14

factSd = 1.3
Apertyre6error = factSd *Sqrt[1/6*Total[(Error6)^2]]
Apertyre14error = factSd *Sqrt[1/6 * Total[(Error14)^2]]

k = 0

screenX = 2*10^k
measurement6 = Function [x, { 10^k*x[[1]]  -screenX,10^k*x[[2]]} ]/@{{22,1.8/7}, {27,2.3/7}, {32,2.2/7}, {37,3/7}} 
measurement14 =  Function [x, { 10^k*x[[1]] - screenX ,10^k*x[[2]]} ]/@{{42,1.9/6},{47,1.1/5}, {52,2.9/7}, {57,2.6/6}}

Fun6   =LinearModelFit[measurement6,{1,x},x]
Fun14 =LinearModelFit[measurement14,{1,x},x]

FittedModel[-1.7099999999999965`*^-8+0.010885714285714276` x]

FittedModel[-1.7099999999999965`*^-8+0.010885714285714276` x]

Plot[Fun6[x],{x,0,10^(-6)*10 },ImageSize -> Large]
Plot[Fun14[x],{x,2*10^-6,10^(-6)*10 },ImageSize -> Large]

kFun6 = D[Fun6[x],x]
kFun14 = D[Fun14[x],x]
EVFun6 = Fun6["EstimatedVariance"]
EVFun14 = Fun14["EstimatedVariance"]

ErrorI6 = Sqrt[(TotalOfApertyre6*EVFun6)^2 + (kFun6*Apertyre6error)^2 ]
ErrorI14 = Sqrt[(TotalOfApertyre14*EVFun14)^2 + (kFun14*Apertyre14error)^2 ]

I6= TotalOfApertyre6 * kFun6
I14 = TotalOfApertyre14 * kFun14
IAvg = (I6 + I14)/2