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Let’s say I have an insect farm and they lay down a lot of eggs, which I collect in a cup.

Now I want to study the size distribution of those eggs, but there’s a problem:

The younger eggs, which are smaller, are denser and dive deep in the cup, while the older eggs are larger (and less dense), so they keep on the top of the cup and are more easily picked. This would introduce a sampling bias towards larger eggs.

So I have an idea: I will lay all of those eggs over a flat table and I’ll pick a group of the smallest ones I can find, and a group of the largest ones I can find.

If I assume the egg sizes are normally distributed, how can I estimate their mean and standard deviation based on the tails of that distribution, as mentioned above?

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    $\begingroup$ Although there is some merit to this idea (it is akin to Ranked Set Sampling, a technique you might want to investigate), you will need additional information: at a minimum, it must include a count of all the eggs, the two group counts, and some quantitative characterization of what constitutes a "group" for purposes of selection. $\endgroup$
    – whuber ♦
    Commented Sep 24, 2020 at 14:25
  • $\begingroup$ @whuber thanks for the insight! I’ll definitely look into the technique you mentioned. $\endgroup$
    – rnahumaf
    Commented Sep 24, 2020 at 14:56

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