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I have a cross-section of 100,000 individuals and information on their age. I suspect that there may be clustering by age or that the sample exhibits behavior that there would be two groups, the old and the young.

Is there a statistical test that tells me the location of the cut-off?

Looking at a histogram, I can eyeball it which occurs at 32 (not 42 incidentally..). But is there a way to test this?

Thanks so much!

Better Plot

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    $\begingroup$ This sounds as if you are asking whether an anti-mode (a local minimum in the density function) is genuine. (I wouldn't use the term cut-off and I don't see what this has to do with the variance.) There are at least three approaches, paralleling similar questions for modes: postulate a model for the distribution as a whole and fit it; see if apparent facts about the data are persistent under resampling; check how the estimated density function changes with different degrees of smoothing. $\endgroup$ – Nick Cox Feb 23 '15 at 22:20
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    $\begingroup$ stats.stackexchange.com/questions/138223/… and similar threads may suggest ideas. $\endgroup$ – Nick Cox Feb 23 '15 at 22:21
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    $\begingroup$ The title of the post does not correspond to the content... $\endgroup$ – Richard Hardy Feb 24 '15 at 8:45
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    $\begingroup$ If your ages run from 30 to 50, then describing those in their 40s as "old" is a poor choice of words, and possibly even insensitive or offensive, although I presume entirely by accident. $\endgroup$ – Nick Cox Feb 24 '15 at 10:49
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    $\begingroup$ Your histogram is badly screwed up. You only have integer age, right? Make each bar width 1, and integer. The gap that you are seeing is due to your bad visualization. There is a drop-off between 33 and 34, but I doubt it is statisticall significant by any measure. I'd say there are no clusters in this chart. $\endgroup$ – Anony-Mousse Feb 24 '15 at 11:12

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