Arithmetic mean

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Arithmetic Mean

The Arithmetic Mean (pronunciation: /ærɪθˈmɛtɪk miːn/), also known as the average, is a measure of central tendency, which is derived by dividing the sum of a set of quantities by the number of quantities in the set.

Etymology

The term "Arithmetic Mean" originates from the Greek word 'arithmos' meaning 'number' and the Latin word 'medius' meaning 'middle'. This term was first used in the 16th century.

Definition

The Arithmetic Mean of a set of numbers is calculated by adding all the numbers in the set, and then dividing the sum by the count of numbers. If the set contains n numbers: a1, a2, a3, ..., an, then the arithmetic mean M is defined as:

M = (a1 + a2 + a3 + ... + an) / n

Related Terms

  • Median: The middle value in a set of numbers.
  • Mode: The most frequently occurring number in a set.
  • Range: The difference between the highest and lowest values in a set.
  • Standard Deviation: A measure of the amount of variation or dispersion in a set of values.
  • Variance: The average of the squared differences from the Mean.

Usage

The Arithmetic Mean is widely used in fields such as mathematics, physics, statistics, and economics. It provides a single value that represents a set of values and is used to calculate the average of a set of numbers.

See Also

External links

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