Mean and standard deviation are more influenced by outliers than median and IQR are. (There are also other location statistics you could use, e.g., for a non-normal distribution it could make more sense to think about the mode of the distribution or some other location parameter for an ex-gaussian or weibull distribution or something like that.) Which summary statistic you need to use depends on what you are trying to show. It is also worth thinking about whether these outliers are truly "outliers" in the sense that they are abnormal data points that don't reflect what you're actually trying to measure (e.g., errors), or whether they're natural data points and thus are reflecting something important about the shape of the distribution.

Dear Beth,

As Stephen correctly says, it really depends what you are trying to show and which statistic best reflects the middle and spread values for your data set. If your data is highly skewed I would tend to use median and inter-quartile range. However, non-normal data does not mean that the mean and standard deviation are not acceptable summary statistics. Have a look at our workshop: http://www.statstutor.ac.uk/resources/uploaded/3descriptive-statisticspdf.zip

Beth,

Non-normal data would generally lean towards median standard deviation; it depends on the shape of the distribution and ultimately what you want to do with it. 

Thanks so much for all your answers. Greatly appreciated.

try this paper

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...