Well its basically this:

x sqrt(x) %inc y sum z

--- ------- ---- ---- ----- ----

10 3.16 50% 4.74 4.74 10

9 3.00 40% 4.20 8.94 20

8 2.83 30% 3.68 12.62 30

7 2.65 20% 3.17 15.79 40

6 2.45 10% 2.69 18.48 50

5 2.24 10% 2.46 20.94 60

4 2.00 20% 2.40 23.34 70

3 1.73 30% 2.25 25.59 80

2 1.41 40% 1.98 27.57 90

1 1.00 50% 1.50 29.07 100

So now I want to find values of say when z is equal to 3, 25, 47,94 etc. Is Interpolation possible? How? And note you cannot do something like the following which is linear Interpolation which is just not accurate.

z sum

--- -----

20 8.94

27 ?

30 12.62

The approximation would be

8.94 + (27-20)/(30-20)*(12.62-8.94) = 8.94 + 0.7*3.68 = 11.516

This is simply 7/10 of the way from 8.95 to 12.62.

Obviously this is not correct. The value for z=27 would be something more than 11.516.