Variable and Variance

noun

• Something that is likely to vary; something that is subject to variation.
  • usage: "the weather is one variable to be considered"
• A quantity that can assume any of a set of values.
  • synonyms: variable quantity
• A star that varies noticeably in brightness.
  • synonyms: variable star
• A symbol (like x or y) that is used in mathematical or logical expressions to represent a variable quantity.

adjective

• Liable to or capable of change.
  • usage: "rainfall in the tropics is notoriously variable"; "variable winds"; "variable expenses"
• Marked by diversity or difference.
  • usage: "the varying angles of roof slope"; "nature is infinitely variable"
  • synonyms: varying
• Used of a device) designed so that a property (as e. G. Light) can be varied. (
  • usage: "a variable capacitor"; "variable filters in front of the mercury xenon lights"

• (n.) Those parts of the sea where a steady wind is not expected, especially the parts between the trade-wind belts.
• (n.) That which is variable; that which varies or is subject to change.
• (a.) Liable to vary; too susceptible of change; mutable; fickle; unsteady; inconstant; as, the affections of men are variable; passions are variable.
• (n.) A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity; as, in the equation x2 - y2 = R2, x and y are variables.
• (a.) Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity.
• (n.) A shifting wind or one that varies in force.

Variable is an element in a model. For example, in the model RS&Pt+1 = a + b Tbill t + et, where RS&Pt+1 is the return on the S&P in month t+1 and Tbill is the Tbill return at month t, both RS&P and Tbill are "variables" because they change through time; i. E., they are not constant.

noun

• An event that departs from expectations.
  • synonyms: discrepancy, variant
• Discord that splits a group.
  • synonyms: division
• The second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value.
• A difference between conflicting facts or claims or opinions.
  • usage: "a growing divergence of opinion"
  • synonyms: discrepancy, disagreement, divergence
• The quality of being subject to variation.
  • synonyms: variability, variableness
• An official dispensation to act contrary to a rule or regulation (typically a building regulation. )
  • usage: "a zoning variance"
• An activity that varies from a norm or standard.
  • usage: "any variation in his routine was immediately reported"
  • synonyms: variation

• (n.) The quality or state of being variant; change of condition; variation.
• (n.) A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, -- as between the writ and the declaration or between the allegation and the proof.
• (n.) Difference that produce dispute or controversy; disagreement; dissension; discord; dispute; quarrel.

Variance is a measure of volatility, risk, or statistical dispersion. It is the square of the standard deviation. The variance is calculated by: computing the mean of the series then taking the deviation or subtracting the mean from each observation, square the differences or deviations for each observation, and divide the sum of the squared deviations by the number of observations. This computation is the precursor to the standard deviation. The standard deviation is calculated by taking the square root of the variance.