I have a numerical dataset in which the standard deviation is larger than the mean and I am interested to know what this fact can tell me about the dataset. I have drawn the following conclusions on my own:
1. The mean is skewed by negative values, extreme outliers or both 2. The dataset is not normally distributed 3. The median will provide a better estimate of a "typical" value than the mean
Can you find any flaw in them? Are there any other conclusions I can draw about this dataset from the fact that the standard deviation is larger than the mean? I'm interested in:
- implications for describing such a dataset, - deciding how "typical" a given value or subset of values from the dataset are, - performing analyses on the dataset as a whole
Sorry if this is overly-vague/theoretical, I have many datasets that I can supply as examples along with specific questions I have about each but I'm choosing to ask a more general question in hopes of getting a deeper understanding about what this phenomena means.