New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!

# Weighted arithmetic mean

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. [1]

## Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

## Average

In colloquial language, an average is a middle or typical number of a list of numbers.

## Bessel's correction

In statistics, Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample.

## Bias of an estimator

In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

## Central tendency

In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.

## Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

## Convex combination

In convex geometry, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.

## Covariance matrix

In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.

## Descriptive statistics

A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics.

## Design matrix

In statistics, a design matrix, also known as model matrix or regressor matrix, is a matrix of values of explanatory variables of a set of objects, often denoted by X. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object.

## Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

## Gauss–Markov theorem

In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator, provided it exists.

## Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

## Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

## Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

## Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.

## Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

## Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.

## Mean

In mathematics, mean has several different definitions depending on the context.

## Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

## Normalizing constant

The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics.

## Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

## Reduced chi-squared statistic

In statistics, the reduced chi-squared statistic is used extensively in goodness of fit testing.

## Simpson's paradox

Simpson's paradox, or the Yule–Simpson effect, is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.

## Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

## Standard error

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation.

## Summary statistics

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible.

## Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

## Weight function

A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.

## Weighted arithmetic mean

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.

## Weighted average cost of capital

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets.

## Weighted geometric mean

In statistics, given a set of data, and corresponding weights, the weighted geometric mean is calculated as Note that if all the weights are equal, the weighted geometric mean is the same as the geometric mean.

## Weighted median

In statistics, a weighted median of a sample is the 50% weighted percentile.

## Weighting

The process of weighting involves emphasizing the contribution of some aspects of a phenomenon (or of a set of data) to a final effect or result, giving them more weight in the analysis.

## References

Hey! We are on Facebook now! »