April 20, 2014

Homework Help: Math - weighted average?

Posted by Kate on Wednesday, October 3, 2012 at 12:15pm.

I need to create some type of formula that will allow me to interpolate values at specific points in a data set. My data is something like this: I have a list of times, and there are values associated with those times like this:

T Readings
1 100 103 105
2 103 101 107
3 102 104 108
4.5 107 107 105
7 105 106 104

I need to correct the times (and the corresponding values) so that each timestamp is one second apart. My professor said that the best way to do this would be with a weighted average.

I'm finding it difficult to find a formula that seems correct. I tried solving for the correct time value, ie:

4 = ((3+4.5)/2)x
Where x= the unknown weight, 4 is the corrected timestamp value, and 3 and 4.5 are the known time values. This gives me an X of 16/15. This process works when I know what the value should be (as with the timestamps), but I don't know what the interpolated reading values should be. I thought that maybe once I found the "weight" from the timestamps I could use it to interpolate the readings, but this doesn't seem to provide a reasonable answer. (ie, plugging in 16/15 for x in the equation ((102+107)/2)x provides a value of 111.47, which doesn't make sense). I also thought about multiplying the average by some sort of percent difference from the target value, but this doesn't seem to work either.

The dataset I have is very large so ideally I'd like to find a formula that I can use in a program to do the calculations for me, rather than doing each calculation by hand. Any help or insight would be appreciated.

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