Here are the data that I want to plot:

```
meandatf1 = Mean /@ datf1
meandatf2 = Mean /@ datf2

{1.48908, 1.49641, 1.49354, 1.50385, 1.49835, 1.49617, 1.50569, \
1.50117, 1.50226, 1.50151, 1.50108, 1.50031, 1.49955, 1.49721, \
1.49898, 1.50266, 1.50177, 1.50227, 1.49886, 1.50002}

{-0.00127783, 0.000556012, 0.0000143709, -0.000602328, -0.000375952, \
-0.00125357, 0.0000228143, 0.000175103, 0.000868018, -0.0003298, \
0.000230178, 0.000222689, -0.0000624273, -0.0000760139, -0.000263302, \
0.0000826082, 0.000206463, 0.0000507921, -0.0000955452, 0.000184107}

```

And here is how I generate my individual plots:

```
genPlot[c_, dat_, ymin_, ymax_, legend_] :=
 ListPlot[{
   Table[c, {Length[dat]}], dat},
   AxesLabel -> {"N", "\[Mu]"}, PlotRange -> {Automatic, {ymin, ymax}},
   PlotLegends -> Placed[legend, Above],
   Joined -> True, Mesh -> None, InterpolationOrder -> 0, 
   ImageSize -> 400] (* I tried also without ImageSize, see below *)

plot1 = genPlot[3/2, meandatf1,  1.45,  1.55,  "\[ScriptCapitalD]1"]
plot2 = genPlot[0,   meandatf2, -0.004, 0.004, "\[ScriptCapitalD]2"]

```

The output of the individual plots is fine:

![enter image description here](https://i.stack.imgur.com/gOVTt.png)

But when I combine the two plots with `GraphicsRow[]` I get this ugly output:

![enter image description here](https://i.stack.imgur.com/vJUfz.png)

When I don't specify `ImageSize` in `genPlot[]` the combined plot is very small (but otherwise looks fine):

![enter image description here](https://i.stack.imgur.com/b3cQJ.png)

If I set `ImageSize` in the `GraphicsRow[]` (and not in `genPlot[]`) the container image is increased instead of the contained cells (which is reasonable, but was a desperate long shot by my side):

![enter image description here](https://i.stack.imgur.com/ARihe.png)

It must be something trivial that I am missing. Any ideas? 

**EDIT1**: I am using *Mathematica* 9.0.1 under Mac OSX Mavericks.

**EDIT2**: Pretty much all of the proposed solutions worked for me. I wish I could accept >1 but, since this is not possible, I'll accept the one from @JasonB for its beauty of simplicity.