Bounded Linear Interpolation

[tprohas]

I have a table of data temperature/resistance data. For a given temperature, the measured x data is bounded by Xlow and Xhigh:
Y Xlow Xhigh
-30 155.2 199.6
-20 85.8 108.39
-10 49.2 61.4

For a measured value of X, what is the best linear interpolation technique to determine f(X)? My assumption is to use the average of Xlow and Xhigh and then do a standard interpolation using the table of Y vs Xavg.

 

[prex]

Can you be more specific on what you intend to do?
Supposing f(X) is your Y, what's the meaning of Xlow and Xhigh? Is this a domain of uncertainty, and, if so, why is it so wide?
If you only know that X is somewhere between Xlow and Xhigh, then your best guess for X is indeed the arithmetic average of Xlow and Xhigh, as you pointed out.
prex
motori@xcalcsREMOVE.com

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[tigrek]

Isnt the least square method for such cases?
Linear - you mean a straight line, I presume, and no curve.
Else, Spline, Bezier etc become relevant too.

 

[tprohas]

RE Prex: The measurements for Xlow and Xhigh are based on the data sheet for a resistive temperature device. Low temperatures will have higher resistance, higher temperatures have lower resistance. Xlow and Xhigh is the uncertainty.

RE Tigrek: I agree with the other methods, but the direction is to use Linear Interpolation. I was wondering if there was a way to use the bounded data to reduce the error in the interpolation techique.

Thanks to all.