Arithmetic Mean Function
An Arithmetic Mean Function is a mean function that divides by the sum of the members.
- Context:
- range: Arithmetic Mean Value.
- It can range from being a Weighted Arithmetic Mean Function to being an Unweighted Arithmetic Mean Function.
- It can range from being an Informal Arithmetic Mean Function to being a Formal Arithmetic Mean Function.
- It can require a conditional function rule for how to behave when the function input is an empty set.
- …
- Example(s):
- [math]\displaystyle{ f_{\text{arithmetic mean}} \left( \frac{1}{4}, \frac{1}{2} \right) }[/math].
- One implemented in a Arithmetic Mean Software Function, such as
statistics.mean(). - …
- Counter-Example(s):
- See: Statistic Function.
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 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.
2017
- https://docs.python.org/3/library/statistics.html#statistics.mean
- QUOTE:
statistics.mean(data)Return the sample arithmetic mean of data which can be a sequence or iterator.
The arithmetic mean is the sum of the data divided by the number of data points. It is commonly called “the average”, although it is only one of many different mathematical averages. It is a measure of the central location of the data.
If data is empty, StatisticsError will be raised.
- QUOTE:
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 …