Interpolating Uncertainties in a time series

So I have a time series formatted as such below:

y1 x1 +/-z1

y2 x2 +/-z2

y3 x3 +/-z3

y4 x4 +/-z4

and I have been trying to linearly interpolate so the resulting data is as such:

y1 x1

y1.5 x1.5

y2 x2

y2.5 x2.5

I have been able to do that using interp1, so I do not have a problem creating the interpolated dataset with x and y, however I an unsure about how to interpolate the uncertainties. Would I just use interp1 again to linearly interpolate the uncertainties corresponding to x1.5 and x2.5? The uncertainty is only in the x values and not the y values if that helps.

Any help would be appreciated!

Nick