data = RandomVariate[NormalDistribution[100, 30], 200];
modData=ReplacePart[data,1->10^6];

Through@{Mean,StandardDeviation}@data
(*{99.529,30.395}*)

Through@{Mean,StandardDeviation}@modData
(*{5098.99,70703.6}*)

Through@{Median,SnDispersion}@modData
(*{99.2765,31.6749}*)

Through@{LinearModelFit,GeneralizedLinearModelFit}[data,{},x]//Normal
(*{99.529,99.529}*)

Through@{LinearModelFit,GeneralizedLinearModelFit}[modData,{},x]//Normal
(*{5098.99,5098.99}*)

GeneralizedLinearModelFit[modData,{},x,DispersionEstimatorFunction->Function[{y,yhat,w},SnDispersion[y-yhat]]]//Normal
(*5098.99*)

GeneralizedLinearModelFit[modData,{},x,DispersionEstimatorFunction->Function[{y,yhat,w},0]]//Normal
(*5098.99*)