Why use standard deviation In what situations is it special?
I will restate your question as "Why are the mean and standard
deviation of a sample so frequently calculated?". The standard
deviation is a measure of the dispersion of the data. It certainly
is not the only measure, as the range of a dataset is also a
measure of dispersion and is more easily calculated. Similarly,
some prefer a plot of the quartiles of the data, again to show data
dispersal.t Standard deviation and the mean are needed when we want
to infer certain information about the population such as
confidence limits from a sample. These statistics are also used in
establishing the size of the sample we need to take to improve our
estimates of the population. Finally, these statistics enable us to
test hypothesis with a certain degree of certainty based on our
data. All this stems from the concept that there is a theoretical
sampling distribution for the statistics we calculate, such as a
proportion, mean or standard deviation. In general, the mean or
proportion has either a normal or t distribution. Finally, the
measures of dispersion will only be valid, be it range, quantiles
or standard deviation, require observations which are independent
of each other. This is the basis of random sampling.