Moments (mathematics)

thumb|400px|right|Example of samples from two populations with the same mean but different variances. The red population has mean and variance (), while the blue population has mean and variance ().

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.

thumb|200px|Example distribution with positive skewness. The data presented is from experiments on wheat grass growth.

in mathematics, a quantitative measure of the shape of a set of points

Kurtosis (from ( or ), meaning 'curved, arching') refers to the degree of tailedness in the probability distribution of a real-valued, random variable in probability theory and statistics. Similar to skewness, kurtosis provides insight into specific characteristics of a distribution. Various methods exist for quantifying kurtosis in theoretical distributions, and corresponding techniques allow estimation based on sample data from a population. Different measures of kurtosis can yield varying interpretations.

concept in probability theory and statistics

parameter estimation technique in statistics

In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa.

moment of a random variable minus its mean

expectation or average of the falling factorial of a random variable

normalized central moments

parameter estimation technique in statistics, particularly econometrics

trying to map moments to a measure that generates them