how to make interpolated data as a function?

For example,

data1 =

0 1 1 2 3 3 5 2 6 2 9 4 11 5 13 6 14 7 16 8

data2 =

0 2 1 3 2 2 3 1 4 2 6 3 8 4 9 6 11 4 16 7

each data have different x-axis interval. so I cannot calculate about these two data set such as multiply each other or dividing each other.

I have to do interpolation and make the data as a function.

how to make it possible?

ex: data1/data2 or data1 x data2

• Please try to write your code in Mathematica syntax Nov 25 '14 at 1:22
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This question is not clear but making a few assumptions this is a direct application of the Interpolation function.

data1 = {0, 1, 1, 2, 3, 3, 5, 2, 6, 2, 9, 4, 11, 5, 13, 6, 14, 7, 16, 8};
data2 = {0, 2, 1, 3, 2, 2, 3, 1, 4, 2, 6, 3, 8, 4, 9, 6, 11, 4, 16, 7};


Now assuming that the data is actually x1,y1,x2,y2,...

xy1 = Partition[data1,2];
xy2 = Partition[data2,2];


Plot it.

ListPlot[{xy1,xy2}]

func1 = Interpolation[xy1, InterpolationOrder -> 1]
func2 = Interpolation[xy2, InterpolationOrder -> 1]

func1[5]/func2[5]

Show[ListPlot[{xy1, xy2}, PlotRange -> All], Plot[{func1[x], func2[x]}, {x, 0, 15}]]