Median, mode, quartiles, quintiles and so on, except when you get to very large number of percentiles.
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The mean is most affected. Mode and Median are not influenced as much by outliers.
there are no limits to outliers there are no limits to outliers
The box and whisker plot informs you of the 5 number summary, which comprises of the minimum and maximum, the median, and the first and third quartiles. The minumum and maximum give you the range, which is not given by measures of central tendancy. also, if it a modified box and whisker plot, outliers will be marked separatley from the rest of the plot, outliers are also not included in the measures of center.
The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
The sample range could be used as an index of dispersion. However, there are objections. One is that this statistic is obviously sensitive to outliers. Another is that for many population distributions there are measures with much better characteristics, even ignoring the problem of outliers.