The graph of the given data points is as follows.

We can approximate the value of as follows.

The slope of the line joining (1, 1) and (2, 3) is given by:

The slope of the line joining (2, 3) and (3,8) is given by:

We average these slopes to find a crude value for :

Average slope

Now for the slope of the slope (i.e. the second derivative):

Slope of slope

Substituting into our radius of curvature formula, we have:

Checking our answer, we can see that the (blue) approximating circle with radius 32.15 passes reasonably closely through our data points. It would be possible to improve on this by taking weighted averages to get more appropriate values for the first and second derivatives.