A past anecdote i learned from the a book;



There are several ways to describe the centre and spread of a distribution. One way to present this information is with a five-number summary. It uses the median as its centre value and gives a brief picture of the other important distribution values. Another measure of spread uses the mean and standard deviation to decipher the spread of data. This technique, however, is best used with symmetrical distributions with no outliers.


Despite this restriction, the mean and standard deviation measures are used more commonly than the five-number summary. The reason for this is that many natural phenomena can be approximately described by a normal distribution. And for normal distributions, the mean and standard deviation are the best measures of centre and spread respectively.


Standard deviation takes every value into account, has extremely useful properties when used with a normal distribution, and is mathematically manageable. But the standard deviation is not a good measure of spread in highly skewed distributions and, in these instances, should be supplemented by other measures such as the semi-quartile range.


The semi-quartile range is rarely used as a measure of spread, partly because it is not as manageable as others. Still, it is a useful statistic because it is less influenced by extreme values than the standard deviation, is less subject to sampling fluctuations in highly skewed distributions and  is limited to only two values Q1 and Q3. However, it cannot stand alone as a measure of spread.