first moment

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first moment

The student calculates the first moment of the data set.

Definition

Noun (Statistics): The expected value or mean of a probability distribution. It is calculated as the sum of the values of a random variable, each multiplied by its probability, or equivalently, as the sum of all observed values divided by the number of values in a sample.

Usage and Examples
  • The first moment about the origin is a measure of central tendency, commonly called the average or mean.
    • In this dataset, the first moment is 15.2, indicating the central location of the distribution.
  • It is the foundational concept for calculating higher-order moments, like variance (the second central moment).
    • Before computing the variance, you must first calculate the first moment of the distribution.
Advanced Usage
  • In physics and engineering, the term "first moment" can refer to a different concept related to force and distance (e.g., the first moment of area). However, in the context of statistics and probability, it exclusively denotes the mean.
    • While in mechanics the first moment is crucial for understanding torque, in statistics it is synonymous with the expected value.
Variants and Related Words
  • Mean (n): The most common synonym for the first moment in statistics.
  • Expected Value (E[X]) (n): The theoretical average of a random variable over many trials; the precise term for the first moment of a probability distribution.
  • Average (n): A more general, often informal, term for the central value.
  • Arithmetic Mean (n): Specifies the method of calculation as a sum divided by the count.
Synonyms
  • Mean
  • Expected Value
  • Average (in a statistical context)
Related Phrases and Concepts
  • Central Moment: A moment calculated about the mean of the distribution. The first central moment is always zero.
  • Raw Moment (or Moment about the origin): A moment calculated about zero. The first raw moment is the mean.
  • Sample Mean: The calculated first moment of a data sample, used as an estimate for the population mean.
first moment

The student calculates the first moment of the data set.

Noun
  1. the sum of the values of a random variable divided by the number of values

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