# Is this a multimodal distribution?

This histogram is part of a task about descriptive statistics. I thought it would be easy, and it is, but i am not sure about this one. First I described this histogram as slightly positively skewed. The skewness coefficient supported this. But then those three peaks caught my eyes and i was confused, because i've learned that it wouldn't make any sense to talk about skewness (or kurtosis) if the distribution is a bimodal or multimodal one. So, my question is one of several. Mainly: Is this a multimodal distribution? Can you say this for sure? Or is this a matter of interpretation? Along these lines the secondary questions are: If it is a multimodal distribution and especially if it is a matter of interpretation, would it be reasonable to describe the skewness, the kurtosis and the seemingly multimodal aspect? Because: from the histogram and the coefficients it seems i could say something about all three aspects. Or is it truely a strict rule, that you can't really talk about skewness/kurtosis, if it is bimodal or multimodal? In this case, i would be back to my initial question: Is this a multimodal distribution and can you be sure?

• Welcome to our site, Arina! This is a very well-posed question. You would likely enjoy glen_b's discussion of ambiguity in histograms in his answer at stats.stackexchange.com/questions/51718. – whuber Jun 2 '15 at 22:45
• Small comment. I take it that the vertical axis is frequency so that the values shown must be integers. Axis labels including 2.5, 7.5, etc. are then not a good choice here. Better would be 0 5 10 15. or 0 4 8 12 16. Less small comment. A normal is not a good reference distribution for a bounded variable. You can see that substantial fractions predicted below 0 and above 100 make that an absurd reference. Naturally, both these details could be default choices from your software. – Nick Cox Oct 6 '17 at 13:48
• – Scortchi - Reinstate Monica Oct 6 '17 at 13:48