for the log-normal distribution here. Angles Particular care is needed when using cyclic data, such as phases or angles. Taking the arithmetic mean of 1° and 359° yields a result of 180°. This is incorrect for two reasons: Firstly, angle measurements are only defined up to an additive constant of 360° ( or , if measuring in radians). Thus, these could easily be called 1° and -1°, or 361° and 719°, since each one of them produces a different average. Secondly, in this situation, 0° (or 360°) is geometrically a better average value: there is lower dispersion about it (the points are both 1° from it and 179° from 180°, the putative average). In general application, such an oversight will lead to the average value artificially moving towards the middle of the numerical range. A solution to this problem is to use the optimization formulation (that is, define the mean as the central point: the point about which one has the lowest dispersion) and redefine the difference as a modular distance (i.e., the distance on the circle: so the modular distance between 1° and 359° is 2°, not 358°). Symbols and encoding The arithmetic mean is often denoted by a bar (vinculum or macron), as in . Some software (text processors, web browsers) may not display the "x̄" symbol correctly. For example, the HTML symbol "x̄" combines two codes — the base letter "x" plus a code for the line above (̄ or ¯). In some document formats (such as PDF), the symbol may be replaced by a "¢" (cent) symbol when copied to a text processor such as Microsoft Word. See also Fréchet mean Generalized mean Geometric mean Harmonic mean Inequality of arithmetic and geometric means Sample mean and covariance Standard deviation Standard error of the mean Summary statistics References Further reading External links Calculations and comparisons between arithmetic mean and geometric mean of two numbers Calculate the arithmetic mean of a series of numbers on fxSolver Means