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 and/or standard:
“Henry David Thoreau, who never earned much of a living or sustained a relationship with any woman that wasn’t brotherly—who lived mostly under his parents’ roof ... who advocated one day’s work and six days “off” as the weekly round and was considered a bit of a fool in his hometown ... is probably the American writer who tells us best how to live comfortably with our most constant companion, ourselves.”
—Edward Hoagland (b. 1932)
“Error is a supposition that pleasure and pain, that intelligence, substance, life, are existent in matter. Error is neither Mind nor one of Mind’s faculties. Error is the contradiction of Truth. Error is a belief without understanding. Error is unreal because untrue. It is that which seemeth to be and is not. If error were true, its truth would be error, and we should have a self-evident absurdity—namely, erroneous truth. Thus we should continue to lose the standard of Truth.”
—Mary Baker Eddy (1821–1910)