Outliers and the standard deviation
The mean and standard deviation are inadequate descriptions of distributions that have clusters, outliers or skewness.
An outlier has a strong influence on the mean of the data and an even bigger effect on the standard deviation. In the data below, one measurement was missing and coded as '999'. If this value (999) is included, the mean is a feasible value, but the standard deviation should be recognised as being unreasonable.
A graphical display such as a dot plot is the best way to detect an outlier and you should always look at the data before summarising with a mean and standard deviation.
An outlier should be carefully examined. Was the value incorrectly recorded? Was there something unusual about the individual from which the measurement was obtained? If we are convinced that there was something wrong about the value, it should be removed from the data set before further analysis.