Assuming that the measurements are on a continuous scale, you would have a lot of mass on the point exactly corresponding to the ruler's length, so you could use something akin to a mode I'd imagine.

The mode should work, right? The length of the ruler is likely to be the only specific value that shows up more than once in the data.

I came up a solution: if we know the distribution of actual measurement and the value of actual measurement, then the expected probability of getting wrong measurement should equal to the probability of actual measurement greater than length of ruler. Not sure this is correct and will interview on friday. good luck to me.

L^{hat} = N/(N+1) * max(X1,X2,X3,...XN) is an unbiased estimator

L^{hat} = 2*sum(X)/N is another unbiased estimator

The length of the ruler would be the censored value in the data. If you draw the histogram of observed values, there should be a mass on the largest value, which is the length of the ruler. The more observation you have, the better the estimation.

I think it should be (N+1)/N * max(X1,..XN). Is there anyone agreeing with me?

If we now the distribution... I'd analyse the tail of cumulative density function.

round(central tendency) * 2

Please ignore my previous two answers above. I misread the question and thought it was a regression problem, when it wasn't.

If we now the distribution... I'd analyse

My initial answer was to use the MAX of the sample. That however is a biased estimator. How can you account for the bias and come up with an unbiased estimator? I think this is where you need to start making assumptions on the distribution. A uniform distribution would allow to estimate the bias.

what kind of distribution is it? what do we do with the data? what precision should we get? what happens if we "lose" the oversize data?

Should first ask whether we have some prior knowledge about the object length distribution