I have a sample where n = 15 and the median = mean but the mode is less.

So I know to be:

  • Positively skewed (mode<median<mean)
  • Negatively skewed (mean<median<mode)
  • Symmetric (mean=median=mode)

But my sample does not fall in any of these categories.

How do I know which way the sample is skewed?

  • 1
    $\begingroup$ Since there are only 15 of them can you edit to show the values? I think i would have said this was positive skew but it might help to confirm that. $\endgroup$
    – mdewey
    Oct 23, 2020 at 15:30
  • $\begingroup$ Just plot a histogram and it should be obvious. $\endgroup$ Oct 23, 2020 at 16:30

1 Answer 1


Those might be useful guidelines, but they aren't rules. The way you determine the skewness is by calculating the skewness. Graphing is another possibility (a USEFUL one), though that will not give you a definitive "the skewness is __".

That said, with a small sample size, I would be skeptical of mild skewness. Higher moments tend to have large standard errors, so the estimate is not precise.


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