"Import the data of a circle with unknown radius R"
SetDirectory[NotebookDirectory[]];

"Check whether the files is in your current Directory[]"
FileExistsQ["datasemicircle.dat"]

"Now, import the file and name it 'rawdata' "
SetDirectory[NotebookDirectory[]];
rawdata=Import["datasemicircle.dat"];
lprawdata=ListPlot[rawdata];
Print[lprawdata]

"Try drawing a semicircle with trial valued R and overlap it on the rawdata circle"
x[t_,R_]:=R*Cos[t];y[t_,R_]:=R*Sin[t];
pp[R_]:=ParametricPlot[{x[t,R],y[t,R]},{t,0,Pi},PlotStyle->Red];
Show[{pp[60.0],lprawdata}]

"How to quantify the error of the trial values of R with respect to the “true” R value of datacircle.dat?"
xrawdata[i_]:=rawdata[[i]][[1]];yrawdata[i_]:=rawdata[[i]][[2]];
Deltari[i_,R_]:=(R^2-(xrawdata[i]^2+yrawdata[i]^2))^2;
ilast=Length[rawdata];
variance[R_]:=Sum[Deltari[i,R],{i,1,ilast}]/Length[rawdata];
std[R_]:=Sqrt[variance[R]];
Plot[std[R],{R,30,70},PlotRange->All,AxesLabel->{r,std}]
Plot[variance[R],{R,30,70},PlotRange->All,AxesLabel->{r,Variance}]