The deviation of a particular number in a set is determined by
subtracting the
mean value of the
set from the number in question. In the study of
statistics, it is often desirable to find the
average deviation of a
set. Unfortunately, when deviation is calculated in the standard manner they will generally cancel each other out when
averaged. Since numbers in the
set will deviate from the
mean both positively and negatively, the standard method of finding the
mean, namely
adding the numbers together and dividing the
sum by the number of numbers in the
set, will yield an answer that's generally near zero. This is not very useful.
To overcome this,
statisticians take each deviation and square it before taking the
mean of the
set of
deviations. This
mean is called the
varience. Taking the
square root of the
varience yields the
standard deviation of the original
set of numbers.