Find barycenter of spectral data

I am trying to find the barycenter of some spectra using numerical integration. I tried to find the wavelength for which the integral splits the spectrum in two equal areas, but the result seems wrong. The code returns the value of about 670 nm, while I was expecting it to be around 663 nm.

Code:

Data = Import["https://pastebin.com/raw/kEQd5uPF", "Table"];
Do[Spec[2*i] = Data[[All, (2*i + 1) ;; (2*i + 2)]], {i, 0, 4}];
[Lambda] = 
  b /. NSolve[
     Integrate[
       Interpolation[Spec[0], InterpolationOrder -> 3][x], {x, 
        Min[Spec[0][[All, 1]]], b}] == 
      Integrate[
       Interpolation[Spec[0], InterpolationOrder -> 3][x], {x, b, 
        Max[Spec[0][[All, 1]]]}], b][[1]];
vertLines = {Thick, ColorData["VisibleSpectrum"][[Lambda]], 
   Line[{{[Lambda], 0}, {[Lambda], Max[Spec[0][[All, 2]]]}}]};
ListPlot[Spec[0], PlotRange -> All, Joined -> True, 
 Prolog -> vertLines]

In the picture, it looks as if the second area is smaller. How can I find the correct barycenter wavelength?

i = 0;
data = Data[[All, (2*i + 1) ;; (2*i + 2)]];
list = 1/2 Table[(data[[i, 2]] + data[[i + 1, 2]])*(data[[i, 1]] - 
   data[[i + 1, 1]]), {i, 1, Length@data - 1}] // Abs;

First@data[[First@First@Position[Accumulate[list], _?(# > Total[list]/2 &), 1, 1]]]
(* 663.336 *)