More questions about symmetry

#1
How can a distribution be symmetric and be positively/negatively skewed? What does reasonably symmetic means? What do they mean by a distribution being relatively normal? Also...if the trimmed mean is different than the mean, does that means there are a lot of extreme scores...(trimmed mean 56.82 and mean 57.57)? Also that distribution have a skewness of .801 and kurtosis of .439...that shows a positive skew. Ugh...confusing!
 

JohnM

TS Contributor
#2
Unless a distribution has a skewness of exactly 0, it is not symmetric. Terms like "reasonably symmetric" and "relatively normal" are merely judgment calls - it's basically up to the researcher.

A trimmed mean is one where extreme / outlier scores have been removed from the distribution - here again, the definition of "outlier" is set by the researcher and may be perceived as arbitrary, and is a judgment call.