A visualization of the PDF together with a red line at the mean point and a blue line at the maximum point

Module[{dist = SmoothKernelDistribution[Transpose[{xValues, yValues}]], 
   meanPoint = Mean[ed2D], maxPoint}, 
  maxPoint = ArgMax[PDF[dist, {x, y}], {x, y}]; 
  Show[Plot3D[Evaluate[PDF[dist, {x, y}]], 
    {x, Min[xValues] - 2 First@dist["Bandwidth"], Max[xValues] + 2 First@dist["Bandwidth"]}, 
    {y, Min[yValues] - 2 Last@dist["Bandwidth"], Max[yValues] + 2 Last@dist["Bandwidth"]}, 
    PlotRange -> All], 
   Graphics3D[{Darker@Red, Thickness[.02], 
    Line[{Append[meanPoint, 0], Append[meanPoint, 0.13]}]}],
   Graphics3D[{Darker@Blue, Thickness[.02], 
    Line[{Append[maxPoint, 0], Append[maxPoint, 0.18]}]}] ]]

from your link.
One can create a WeightedData object using

from your link.
There a two possible interpretations for these data points.

Interpretation as univariate distribution

Interpreting the yValues as weights and finding the most probable xValue as the objective.
One can create a WeightedData object using

Interpretation as multivariate distribution

Interpreting the xValues and yValues as 2D data points and with "finding the most probable {x,y} data point" as the objective.
One can create an EmpiricalDistribution object

ed2D = EmpiricalDistribution[Transpose[{xValues, yValues}]]

and then calculate its mean with

Mean[ed2D]

{-0.227361, 1.88819}