Write the characteristics of arithmetic mean of a distribution
Answers
Answer:
In mathematics and statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk ˈmiːn/, 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.[1] 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.
Answer:
It should be rigidly defined so as to avoid different people choosing different values for the same measure of central tendency.
It should be easily comprehensible and easy to calculate.
It should be based upon all observations.
It should be amenable for further mathematical treatment.
It should be affected as little as possible by the presence of extreme values.
It should be least affected by sampling fluctuation, i.e., an ideal measure of central tendency should not vary in its value too much from one sample to another when all the samples are taken from the same set of observations.
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