What is standard deviation? Why is it called that?
It is a measure of the expected distance between an element of a set and the set's mean.
The standard deviation of a set of numbers can be thought of as how far, on average, each number in the set is from the mean of the set. In other words, if we pick a number from a set at random, the mean tells us what we should expect that number to be, and the standard deviation tells us how far we should expect that number to be from the mean.
For a random variable
#mu = E[X] = 1/n sum_(i=1)^n x_i#
The standard deviation
#sigma = sqrt(E[(X-mu)^2])=sqrt(1/n sum_(i=1)^n(x_i- mu)^2#
(The square/square root is necessary because we want to calculate a positive average distance, and some of the elements in our set are below
For probability distributions (as well as data sets), the standard deviation is a measure of the spread of the distribution (data). The larger
In the name "standard deviation":
Hence, the standard deviation of a set measures the typical distance between elements of the set and the set's average.