Question

Of the range and the standard deviation, which is more widely used in statistical analysis, and why?

Answer 1

Standard deviation is most widely used.

Range simply gives the difference between lowest and highest value, and a few extreme values will alter the range excessively.

The standard deviation `sigma` tells you where most of the values will be, and in a normal distribution 68% of all values will be within one standard deviation from the mean `mu`, and 95% will be within two standard deviations of the mean.

Example:
You have a filling machine that fills kilogram bags of sugar. It will not fill exactly `1000g` every time, the standard deviation is `10g`.
Then you know, that `68%` is between `990and1010g`, and `95%` between `980and1020g`, a total span of `20g` or `40g` respectively.

Every now and again a bag will be far over-filled (say `1100g`) and sometimes a bag will end up empty (`0g`), so the range will be a total of `1100g`.

You may decide which of the two gives a better idea of the spread in this distribution.