Assertion: arithmetic mean | /r/HasProperty | equal
Facets:
value: to 1
type: OTHER
value: to infinity
type: OTHER
value: unlike the finite case
type: OTHER
value: to the population
type: OTHER
Source sentences:
text: The sample mean x ¯ {\displaystyle {\bar {x}}} (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator).
text: Unlike the finite case, the expectation here can be equal to infinity, if the infinite sum above increases without bound.
text: (in which case the first arithmetic mean and first geometric mean are both equal to x 1 , and similarly with the second arithmetic mean and second geometric mean); and in the second inequality, the two sides are only equal if the two geometric means are equal.
text: In such settings, a desirable criterion for a "good" estimator is that it is unbiased; that is, the expected value of the estimate is equal to the true value of the underlying parameter.