w1  =  {{1, 1.6}, {2, 1.65}, {3, 1.6}, {4,  1.8}, {5,  2.1}, {6, 
          2.2}, {7, 2.0}, {8, 1.5}, {9, 1.3}, {10, 1.4}}

Interp[i_]  := (w1[[i - 1]] + w1[[i + 1]])/
        2
Average[p1_, p2_]  :=  (p1 + p2)/2
Smooth[i_] :=  Average[w1[[i]], Interp[i]]

For[j = 1; w2 = {}, j < 11, j++, 
      If[j == 1, w2 = Append[w2, w1[[1]]], 
        If[j == 10, w2 = Append[w2, w1[[10]]], 
          w2 = Append[w2, Smooth[j]]]]]

w2

g1 = 
      Graphics[{PointSize[0.025], Thickness[0.01], RGBColor[0, 0, 0], 
          Line[w1]}]

g2  =  
      Graphics[{PointSize[0.025], Dashing[{0.01, 0.02}], Thickness[0.01], 
          RGBColor[0.3, 0.3, 0.3], Line[w2]}]

Show[{g1, g2}, Axes -> Automatic]

Show[g1, Axes -> Automatic]