You'll never change your opinion because you refuse to understand the science.
Of COURSE they don't get 100% coverage:
THAT IS WHY THE ERROR BARS ARE LARGER!!!
In your house example, you just INCREASE THE ERROR estimations. You look at the trends in your linked graph, and you can see they all trend similarly: not in lockstep, but if you can see those trends/associations visually, then it's far easier to trend them using actual math.
A better representation (where you can SEE the small European MWP and LIA are NOT global events) is also visible:
If you have 80% to 90% coverage, you CAN get decent data from it; just because there are gaps doesn't make it useless data (but apparently you seem to think so). And you STILL have not admitted that temperatures of the past 10 years being 0.2°C higher have pushed the present day temps ABOVE the error bars. If you cannot accept simple scientific facts, then stop wasting people's time here. THIS THREAD IS ABOUT THE SCIENCE, NOT YOUR 'VERSION' OF IT. If you don't like the data the PAGES2K group put together, then SEND THE QUESTIONS TO THEM. I strongly doubt you will understand a single paragraph of what you get back...
If you have a math degree, I cannot fathom how you never learned anything about error bars and error ranges in any form of statistics. You must have skipped that semester, done too much weed, or simply been a very mediocre student.