Can the standard deviation of non-negative data exceed the mean?

I have some triangulated 3D meshes. The statistics for the triangle areas are:

  • Min 0.000
  • Max 2341.141
  • Mean 56.317
  • Std dev 98.720

So, does it mean anything particularly useful about the standard deviation or suggest there are bugs in calculating it, when the figures work out like the above? The areas are certainly far from being normally distributed.

And as someone mentioned in one of their responses below, the thing that really surprised me that it only took one SD from the mean for the numbers to go negative and thus out of the legal domain.

Thanks

Answer

There is nothing that states that the standard deviation has to be less than or more than the mean. Given a set of data you can keep the mean the same but change the standard deviation to an arbitrary degree by adding/subtracting a positive number appropriately.

Using @whuber’s example dataset from his comment to the question: {2, 2, 2, 202}. As stated by @whuber: the mean is 52 and the standard deviation is 100.

Now, perturb each element of the data as follows: {22, 22, 22, 142}. The mean is still 52 but the standard deviation is 60.

Attribution
Source : Link , Question Author : Andy Dent , Answer Author : varty

Leave a Comment