legend={text={ multi line

What always works in such cases is to add a simple tabular.

documentclass[tikz,border=3mm]{standalone}
usetikzlibrary{datavisualization}
usetikzlibrary{datavisualization.formats.functions}
begin{document}
begin{tikzpicture}
datavisualization[scientific axes=clean]
  [
  visualize as smooth line=Gaussian,
  Gaussian={pin in data={text={$e^{-x^2}$},when=x is 1}}
  ]
  data [format=function] {
      var x : interval [-7:7] samples 51;
      func y = exp(-value x*value x);
  }
  [
  visualize as scatter,
  legend={south east outside},
  scatter={
      style={mark=*,mark size=1.4pt,text width=1.5cm,cells={align=left}},
      label in legend={text={begin{tabular}[t]{l}
  $sumlimits_{i=1}^{10} x_i$, where         
  $x_i sim U(-1,1)$
  end{tabular}}}}
  ]
  data [format=function] {
      var i : interval [0:1] samples 20;
      func y = 0;
      func x = (rand + rand + rand + rand + rand +
      rand + rand + rand + rand + rand);
  };
end{tikzpicture}
end{document}

If you have more of those, you may want to change the node styles.

documentclass[tikz,border=3mm]{standalone}
usetikzlibrary{datavisualization}
usetikzlibrary{datavisualization.formats.functions}
begin{document}
begin{tikzpicture}[cells={nodes={align=left}}]
datavisualization[scientific axes=clean]
  [
  visualize as smooth line=Gaussian,
  Gaussian={pin in data={text={$e^{-x^2}$},when=x is 1}}
  ]
  data [format=function] {
      var x : interval [-7:7] samples 51;
      func y = exp(-value x*value x);
  }
  [
  visualize as scatter,
  legend={south east outside},
  scatter={
      style={mark=*,mark size=1.4pt,text width=1.5cm,cells={align=left}},
      label in legend={text={$sumlimits_{i=1}^{10} x_i$, where         
  $x_i sim U(-1,1)$}}}
  ]
  data [format=function] {
      var i : interval [0:1] samples 20;
      func y = 0;
      func x = (rand + rand + rand + rand + rand +
      rand + rand + rand + rand + rand);
  };
end{tikzpicture}
end{document}

In any case, it would be great if you could in the future provide complete documents that start with documentclass, end with end{document} and contain just enough packages and libraries to be compiled. This makes it easier to look at your question(s).