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No. Outliers are part of the data and do not affect them. They will, however, affect statistics based on the data and inferences based on the data.
the interquartile range is not sensitive to outliers.
The range is very sensitive to outliers. Indeed if there are outliers then the range will be unrelated to any other elements of the sample.
there are no limits to outliers there are no limits to 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.