Consider a list of 100 data points (they happen to be my finishing times for playing crossword puzzles) sorted from earliest to latest. Assume the general trend is upward.

Now consider that a contiguous block of 20 of the data points is in fact missing. For example, I have the values for 1 - 35 and I have the values for 56 through 100, but I do not have the values for 36 through 55.

What is the most mathematically sensible way to fill in those 20 missing values?

It occurs to me that there are two possibilities. In the simpler one, a single value is calculated and used for all 20 of the missing data points. If that's the better possibility, how do I calculate that value?

The other possibility, unlike the one above, would somehow account for trends by filling in the missing 20 values with a series of different values based on the known values before and after the gap. If this is the better possibility, how do I calculate those missing values?

(The real-world example of this problem, in case it helps, can be seen in Excel 2000 format at http://barelybad.com/xwd_times_194.xls. The gap starts at Row 173 and continues to Row 204.)

So, to repeat, what is the most defensible way of somehow filling in those 20 missing values, and what is the rationale?

I've tried to noodle it out several times over the last couple years, and now I'm turning to experts for help.

Thanks for any ideas you can offer.

--Johnny

johnegee aattt gmail ddoottt ccommm