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

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

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Answer 1 · 2015-02-09T01:57:17

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.

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

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