In[1]:= NumLessThan[x_, data_] := (i = 1;
  For[i := 1, x > data[[i]] && i <= Length[data], i++, i]; i - 1)

In[2]:= CDFDisc[x_, data_] := NumLessThan[x, Sort[data]]/Length[data]

In[3]:= data =
 RandomVariate[NormalDistribution[],
  2]; Plot[{CDF[NormalDistribution[], x], CDFDisc[x, data]}, {x, -5,
  4}]

In[4]:= NIntegrate[
 Abs[CDF[NormalDistribution[], x] - CDFDisc[x, data]], {x, -10, 10}]

Out[4]= 10.

In[5]:= Plot[
 Abs[CDF[NormalDistribution[-0.5, 1], x] - CDFDisc[x, data]], {x, -10,
   10}, PlotRange -> Full]

In[6]:= NIntegrate[CDF[NormalDistribution[], x], {x, -10, 10}]

Out[6]= 10.