Arithmetic mean

The arithmetic mean is the sum of a set of numerical values divided by the number of values. It is the familiar average that balances deviations above and below it.

Summation: Summation is the addition of a sequence of terms, often written with sigma notation. Adding every observation is the first step in the arithmetic mean’s defining calculation.
Linearity of expectation: Linearity of expectation states that the expected value of a sum equals the sum of expected values. It follows the same additive structure as the arithmetic mean.
Median: The median is the middle value of an ordered dataset, or the midpoint of its two middle values. It resists extreme observations that can strongly shift the arithmetic mean.
Sample mean: The sample mean is the arithmetic mean of observations selected from a population. It uses the same calculation to estimate a population’s average.
Sample size: Sample size is the number of observations included in a sample or dataset. The mean divides the total by precisely this count.
Least squares: Least squares estimates parameters by minimizing the sum of squared residuals. For a single constant fitted to data, least squares selects the arithmetic mean.
Mode (statistics): The mode is the most frequently occurring value in a dataset. It summarizes frequency rather than balancing the numerical values.
Population mean: The population mean is the arithmetic average of every value in a defined population. It is the full-population counterpart to a mean calculated from a sample.
Numerical data: Numerical data are observations represented as numbers on which arithmetic operations can be performed. The arithmetic mean applies to numerical values, unlike averages for categorical data.
Mean absolute deviation: Mean absolute deviation is the average absolute distance of observations from a reference value. Using absolute rather than squared distances makes the median, not the mean, the minimizing center.

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