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so understanding what unimodal, bimodal & multimodal distributions mean was easy, but I wonder how strict should I be when I am applying the definitions to real data, in that sense, I need to ask, does the peak at 4 in the histogram below large enough to consider the distribution bimodal? if yes, is the other peak at 10 large enough to consider the curve actually multimodal?

I wonder if whenever I find a peak, no matter how small it is, should I consider it or if peaks at certain sizes can be too small and considered negligible.

Distribution

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marked as duplicate by Scortchi Mar 16 '18 at 8:20

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  • $\begingroup$ There is just too little data to tell. Your second mode is based on just two observations. Consider the distribution to be not yet known with probably one peak at 7 and gather more data. $\endgroup$ – Bernhard Mar 16 '18 at 7:05
  • $\begingroup$ @Bernhard Thank you for answering. I know the data is limited, but this is what I got since I have an assignment with this data and I have to describe the distribution based on them (p.s: I am sure you meant my second mode is made of 4 observation, but I know it is too little) $\endgroup$ – Ammar Aldawoodyeh Mar 16 '18 at 7:12
  • $\begingroup$ No, I mean literally two observations: Take two away and the "mode" disappears. Change one to a 3 and one to a 5 and your peak becomes a valley. You do not have a distribution here but observations from a distribution and you have to little observations to claim more, then that there appears to be one mode somewhere in the middle and the rest is unknown. $\endgroup$ – Bernhard Mar 16 '18 at 8:03
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Strictly speaking, your histograms (!) are bimodal and multimodal.

Then again, you seem to have non-integer data, as indicated by the small bar at 7.5. On the one hand, this makes me wonder why there are spaces between the other bars.

On the other hand, and this is the important part, this means that your histogram's appearance will depend heavily on how you define the bins. Try plotting histograms with bin widths of 1.0 or 0.1 instead of the 0.5 you seem to be having. You will get very different results, in particular given the small amount of data you have. Alternatively, run a kernel density estimate over your data, with different kernel bandwidths. Here is a possibly enlightening discussion of a similar effect.

In the end, whether you should treat your data as uni-, bi- or multimodal will depend on what you want to do with it. In the present case, I would say that you have far too few data points to estimate two or mode modes with any precision, so even if the underlying (unknown!) distribution is multimodal, it probably makes sense to only fit a unimodal distribution.

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  • $\begingroup$ Thank you for the reply! I drew the second histogram just to illustrate that there could be a third peak (as demonstrated by the red line I made) $\endgroup$ – Ammar Aldawoodyeh Mar 16 '18 at 7:57
  • $\begingroup$ the spaces between the bars are the results of how the participants answered the question. all of them answered the question, which was "how many hours do you sleep" using integers, except for one of them who answered 7.5 . I'll educate myself about kernel density. Please note it is not me that collected the data, it's just part of an assignment that I was given and was asked to describe, so I just wanted to make sure if my worry about the second mode is justified. Thanks for the informative answer! $\endgroup$ – Ammar Aldawoodyeh Mar 16 '18 at 8:04

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