# Mean

mean valuepopulation meanaverageaveragedmean vectormeansArithmetic meanaverage of any integrable functioncentral tendencyexpected
There are several kinds of mean in various branches of mathematics (especially statistics).wikipedia
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### Statistics

statisticalstatistical analysisstatistician
There are several kinds of mean in various branches of mathematics (especially statistics). In probability and statistics, the population mean, or expected value, are a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation).

### Arithmetic mean

meanaveragearithmetic
For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.
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 count of numbers in the collection.

### Average

Rushing averageReceiving averagemean
For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.
The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.

### Mode (statistics)

modemodalmodes
In descriptive statistics, the mean may be confused with the median, mode or mid-range, as any of these may be called an "average" (more formally, a measure of central tendency).
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.

### Median

averagesample medianmedian-unbiased estimator
In descriptive statistics, the mean may be confused with the median, mode or mid-range, as any of these may be called an "average" (more formally, a measure of central tendency).
The median is a popular summary statistic used in descriptive statistics, since it is simple to understand and easy to calculate, while also giving a measure that is more robust in the presence of outlier values than is the mean.

### Skewness

skewedskewskewed distribution
The mean of a set of observations is the arithmetic average of the values; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or the most likely value (mode).
In the older notion of nonparametric skew, defined as where \mu is the mean, \nu is the median, and \sigma is the standard deviation, the skewness is defined in terms of this relationship: positive/right nonparametric skew means the mean is greater than (to the right of) the median, while negative/left nonparametric skew means the mean is less than (to the left of) the median.

### Exponential distribution

exponentialexponentially distributedexponentially
While the median and mode are often more intuitive measures for such skewed data, many skewed distributions are in fact best described by their mean, including the exponential and Poisson distributions.
where β > 0 is mean, standard deviation, and scale parameter of the distribution, the reciprocal of the rate parameter, λ, defined above.

### Cauchy distribution

LorentzianCauchyLorentzian profile
Not every probability distribution has a defined mean; see the Cauchy distribution for an example.
The Cauchy distribution is an example of a distribution which has no mean, variance or higher moments defined.

### Descriptive statistics

descriptivedescriptive statisticstatistics
In descriptive statistics, the mean may be confused with the median, mode or mid-range, as any of these may be called an "average" (more formally, a measure of central tendency).
Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness.

### Quasi-arithmetic mean

generalised f-meangeneralized ''f''-meangeneralized ƒ-mean
This can be generalized further as the generalized ƒ-mean
In mathematics and statistics, the quasi-arithmetic mean or generalised f-mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function f. It is also called Kolmogorov mean after Russian mathematician Andrey Kolmogorov.

### Generalized mean

power meangeneralisedHölder generalized mean
The generalized mean, also known as the power mean or Hölder mean, is an abstraction of the quadratic, arithmetic, geometric and harmonic means.
In mathematics, generalized means are a family of functions for aggregating sets of numbers, that include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means).

### Truncated mean

trimmed meanmodified mean
In this case, one can use a truncated mean.
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median.

### Mean of circular quantities

circular meancircular averagingcircular means
You can do this by adjusting the values before averaging, or by using a specialized approach for the mean of circular quantities.
In mathematics, a mean of circular quantities is a mean which is sometimes better-suited for quantities like angles, daytimes, and fractional parts of real numbers.

### Geometric mean

geometric averagegeometricmean
The geometric mean is an average that is useful for sets of positive numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean); e.g., rates of growth.
In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

### Central tendency

Localitycentral locationcentral point
In descriptive statistics, the mean may be confused with the median, mode or mid-range, as any of these may be called an "average" (more formally, a measure of central tendency). In probability and statistics, the population mean, or expected value, are a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.

### Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
In probability and statistics, the population mean, or expected value, are a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a continuous distribution,the mean is, where f(x) is the probability density function.
Student's t distribution, the distribution of the ratio of a standard normal variable and the square root of a scaled chi squared variable; useful for inference regarding the mean of normally distributed samples with unknown variance (see Student's t-test)

### Probability density function

probability densitydensity functiondensity
For a continuous distribution,the mean is, where f(x) is the probability density function.
For instance, the above expression allows for determining statistical characteristics of such a discrete variable (such as its mean, its variance and its kurtosis), starting from the formulas given for a continuous distribution of the probability.

### Contraharmonic mean

contraharmonic mean filter
Contraharmonic mean
The contraharmonic mean is a special case of the Lehmer mean, L_p, where p = 2.

### Poisson distribution

PoissonPoisson-distributedPoissonian
While the median and mode are often more intuitive measures for such skewed data, many skewed distributions are in fact best described by their mean, including the exponential and Poisson distributions.
If N electrons pass a point in a given time t on the average, the mean current is I=eN/t; since the current fluctuations should be of the order (i.e., the standard deviation of the Poisson process), the charge e can be estimated from the ratio.

### Grand mean

grand average
Grand mean
The grand mean is the mean of the means of several subsamples, as long as the subsamples have the same number of data points.

### Interquartile mean

interquartile
The interquartile mean is a specific example of a truncated mean.
We now have 6 of the 12 observations remaining; next, we calculate the arithmetic mean of these numbers:

### Normal distribution

normally distributednormalGaussian
If the population is normally distributed, then the sample mean is normally distributed:
\mu is the mean or expectation of the distribution (and also its median and mode),

### Weighted arithmetic mean

averageaverage ratingweighted average
The weighted arithmetic mean (or weighted average) is used if one wants to combine average values from samples of the same population with different sample sizes:
Mean

### Taylor's law

Taylor's power lawvariance to mean power law
Taylor's law
Taylor's law (also known as Taylor's power law) is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship.

### Neuman–Sándor mean

Neuman–Sándor mean
Mean