# Mean

**mean valueaveragepopulation meanaveragedmean vectorArithmetic meanmeansaverage of any integrable functioncentral tendencyexpected**

There are several kinds of means in various branches of mathematics (especially statistics).wikipedia

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### Statistics

**statisticalstatistical analysisstatistician**

There are several kinds of means in various branches of mathematics (especially statistics). In probability and statistics, the population mean, or expected value, is 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.

In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.

### 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.

### Cauchy distribution

**LorentzianCauchyLorentzian distribution**

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.

### Central tendency

**LocalityLocality (statistics)Measure of central tendency**

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, is a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.

### Quasi-arithmetic mean

**generalised f-meangeneralized ''f''-meangeneralised ''f''-mean**

This can be generalized further as the generalized f-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 meanHölder meangeneralised**

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 meanOlympic average**

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).

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

In probability and statistics, the population mean, or expected value, is 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.

### 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**

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

### Grand mean

**grand averagePooled mean**

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

### 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.

### 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 distributedGaussian distributionnormal**

If the population is normally distributed, then the sample mean is normally distributed:

### Taylor's law

**Morisita’s index of dispersionTaylor's power lawTaylor’s power 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.

### 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: