mean
Sign in to saveA mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.
Article
23 sectionsContents
- Types of means
- Pythagorean means
- Arithmetic mean (AM)
- Geometric mean (GM)
- Harmonic mean (HM)
- Relationship between AM, GM, and HM
- Statistical location
- Mean of a probability distribution
- Generalized means
- Power mean
- Quasi-arithmetic mean
- Weighted arithmetic mean
- Truncated mean
- Interquartile mean
- Mean of a function
- Mean of angles and cyclical quantities
- Fréchet mean
- Triangular sets
- Swanson's rule
- Other means
- See also
- Notes
- References
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.
The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted using an overhead bar, \bar{x}. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the sample mean (\bar{x}) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x.