In[]:=
(*interpolationworkswith3Ddata*)​​d=RandomReal[{0,10},{100,3}];​​f=Interpolation[d,InterpolationOrder->1]​​f[5,5]
Out[]=
InterpolatingFunction
Domain: {{0.162,9.87},{0.0727,9.99}}
Output: scalar

Out[]=
6.08424
In[]:=
(*interpolationworkswith4Ddata*)​​d=RandomReal[{0,10},{1000,4}];​​f=Interpolation[d,InterpolationOrder->1]​​f[5,5,5]
Out[]=
InterpolatingFunction
Domain: {{0.00204,10.},{0.00441,9.99},{0.0122,10.}}
Output: scalar

Out[]=
5.30088
In[]:=
d=RandomReal[{0,10},{1000,5}];​​f=Interpolation[d,InterpolationOrder->1]​​f[5,5,5,5]
Interpolation
:The coordinates do not lie on a structured tensor product grid.