Since it looked to me that the median value was the correct distance measurement, that is what I went with.

I am using the code from this blog post http://forum.arduino.cc/index.php?topic=53081.msg1160999#msg1160999

The code did not handle the float values for voltage measurement, so I used the raw analog input, resampled the data, and plugged the raw input into the fast mean code.

Here is the data from the raw analog numbers:

This is the data with some outliers:

This is the data with the large outliers removed:

and because I wasn't having much luck getting a good measurement with distances less than 10", this is the data from 10 to 60in:

Call:
lm(formula = newPinData$distance ~ newPinData$pin_measurement + 
    I(newPinData$pin_measurement^2) + I(newPinData$pin_measurement^3))

Coefficients:
                    (Intercept)       newPinData$pin_measurement  
                      8.992e+01                       -6.168e-01  
I(newPinData$pin_measurement^2)  I(newPinData$pin_measurement^3)  
                      1.796e-03                       -1.805e-06