Relationship Between Standard Deviation and Mean
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point. The precise statement is the following: suppose x1, ..., xn are real numbers and define the function:
Using calculus or by completing the square, it is possible to show that σ(r) has a unique minimum at the mean:
Variability can also be measured by the coefficient of variation, which is the ratio of the standard deviation to the mean. It is a dimensionless number.
Read more about this topic: Sample Standard Deviation
Famous quotes containing the words relationship between, relationship and/or standard:
“It would be a fallacy to deduce that the slow writer necessarily comes up with superior work. There seems to be scant relationship between prolificness and quality.”
—Fannie Hurst (1889–1968)
“Friendship is by its very nature freer of deceit than any other relationship we can know because it is the bond least affected by striving for power, physical pleasure, or material profit, most liberated from any oath of duty or of constancy.”
—Francine Du Plesssix Gray (20th century)
“Society’s double behavioral standard for women and for men is, in fact, a more effective deterrent than economic discrimination because it is more insidious, less tangible. Economic disadvantages involve ascertainable amounts, but the very nature of societal value judgments makes them harder to define, their effects harder to relate.”
—Anne Tucker (b. 1945)