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In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. [ 1 ] It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data), [ 2 ...
If = (+) is rational, then = is also rational, which is a contradiction if it is already known that the square roots of all non-square natural numbers are irrational. Minimal polynomial The golden ratio φ and its negative reciprocal − φ −1 are the two roots of the quadratic polynomial x 2 − x − 1 .
Squared deviations from the mean (SDM) result from squaring deviations.In probability theory and statistics, the definition of variance is either the expected value of the SDM (when considering a theoretical distribution) or its average value (for actual experimental data).
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n.
A little algebra shows that the distance between P and M (which is the same as the orthogonal distance between P and the line L) (¯) is equal to the standard deviation of the vector (x 1, x 2, x 3), multiplied by the square root of the number of dimensions of the vector (3 in this case).
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15.
The square root of 2 (approximately 1.4142) is a real number that, when multiplied by itself or squared, equals the number 2.It may be written in mathematics as or /.It is an algebraic number, and therefore not a transcendental number.