# Arithmetic Mean Value

An Arithmetic Mean Value is a mean value calculated by an arithmetic mean function for some population.

**Context:**- It can range from being a Population Arithmetic Mean Value to being a Sample Arithmetic Mean Value.
- It can be a Weighted Arithmetic Mean Value (for a weighted arithmetic mean function).

**Example(s):**- [math]\displaystyle{ \frac{3}{8} }[/math] for [math]\displaystyle{ f_{\text{arithmetic mean}} \left( \frac{1}{4}, \frac{1}{2} \right) }[/math].
- …

**Counter-Example(s):****See:**Geometric Mean, Harmonic Mean, Law of Large Numbers, Arithmetic Median.

## References

### 2018

- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/arithmetic_mean Retrieved:2018-10-27.
- 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. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean.In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.

While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values). Notably, for skewed distributions, such as the distribution of income for which a few people's incomes are substantially greater than most people's, the arithmetic mean may not coincide with one's notion of "middle", and robust statistics, such as the median, may be a better description of central tendency.

- In mathematics and statistics, the

### 2009

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Arithmetic_mean
- … If the list is a statistical population, then the mean of that population is called a population mean. If the list is a statistical sample, we call the resulting statistic a sample mean.
The mean is the most commonly-used type of average and is often referred to simply as the average. The term "mean" or "arithmetic mean" is preferred in mathematics and statistics to distinguish it from other averages such as the median and the mode. …

- … If the list is a statistical population, then the mean of that population is called a population mean. If the list is a statistical sample, we call the resulting statistic a sample mean.

### 2005

- (Lord et al., 2005) ⇒ Dominique Lord, Simon P. Washington, and John N. Ivan. (2005). “Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory.” In: Accident Analysis & Prevention, 37(1). doi:10.1016/j.aap.2004.02.004
- QUOTE: The mean and variance of the binomial distribution are [math]\displaystyle{ E(Z) = Np }[/math] and [math]\displaystyle{ VAR(Z) = Np(1-p) }[/math] respectively.

### 1921

- (Gini, 1921) ⇒ Corrado Gini. (1921). “Measurement of Inequality of Incomes.” The Economic Journal 31, no. 121 DOI:10.2307/2223319
- QUOTE: … In the first of these the relations are brought to light which exist between the mean deviation from the arithmetic mean, the mean deviation from the median, and the area of concentration. …

### 1920

- (Dalton, 1920) ⇒ Hugh Dalton. (1920). “The Measurement of the Inequality of Incomes.” The Economic Journal 30, no. 119
- QUOTE: … The arithmetic mean is, indeed, easily calculated from perfect statistics, and fairly easily approximated to from imperfect statistics, but the corresponding calculations for the geometric and harmonic means are very laborious, when the number of individual incomes is large …