Question

Which measure of dispersion is the most unstable statistic and why?

Answer 1

Range is the most unstable statistic because:

1. The range is not based on all the terms. Only extreme items reflect its size. Hence, range cannot be completely representative of the data as all other middle values are ignored.
2. Due to the above reason, the range is not a reliable measure of dispersion.
3. Range does not change even the least even if all other, in between, terms and variables are changed.
4. The range is too much affected by the fluctuation of sampling. Range changes from sample to sample. As the size of sample increases range increases and vice-versa.
5. It does not tell us anything about the variability of other data.
6. For open-end intervals, range is indeterminate because lower and appear limits of first and last interval are not given.