I think you're missing the point about the calculated mean, and by implication you're inferring they stopped calculating it after a certain day
because conditions had changed and they were trying to cover something up.

Think of it like the height of a river, sometimes it's high, other times its low, but it's all relative. So you pick some index day, perhaps one of no significance of it's own, and call the water depth that day zero, and refer all other values as either + or - that value. Or to avoid picking a day that might have been extraordinarily wet or dry, you average a whole bunch of days and call that average zero. There is no significance to that particular number, or the range which you averaged, it's just an arbitrary mark on the wall other measurements are referenced to, and it certainly isn't some sneaky way of fooling people for some sinister purpose.

The NSIDC charts now don't have any averages, so this criticism isn't an issue, they simply graph the monthly sea ice against the year, and then draw a regression line through the points ( a purely objective statistical analysis procedure, and very common in the sciences when trying to reveal a legitimate phenomenon lurking in noisy data, but even this can be misleading, as you point out. In this case, though, the phenom isn't lurking, and the data's not that noisy. It jumps out at you.

For starters, areas frozen vary enormously due to the season of the year, there simply is more ice in winter than summer. Also, what do we mean by "frozen"? Solid enough to drive a truck on? Or 85% or more covered by pack, berg or floe ice? Also, how do we take the measurement? Do the Feb graph points show the greatest (or lowest) ice extent for each Feb, or the ice extent on midnight Feb 14th? Or the average of every measurement taken in Feb? It probably doesn't matter as long as you use the same protocol every time you repeat the measurement.

But it really seems to me you are suggesting that either deliberately or subconsciously, researchers are picking a protocol which most favors a controversial conclusion, one which you reject, and they are trying to promote. This is what pushes my buttons. Short of getting all the raw data myself from the researchers and subjecting it to every bit of analysis I know, I'm not going to set out to prove they are right or wrong just to satisfy myself. I have neither the time nor inclination to do this on my time off, it simply isn't that important to me and I just don't think they have enough of a motivation to do something that dishonest, especially if they don't even consciously realize they're doing it.