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The absolute value of z represents the distance between that raw score x and the population mean in units of the standard deviation. z is negative when the raw score is below the mean, positive when above. Calculating z using this formula requires use of the population mean and the population standard deviation, not the sample mean or sample ...
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
Norm (mathematics) In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space ...
Probability theory. In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while ...
The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...
The Mandelbrot set (/ ˈmændəlbroʊt, - brɒt /) [1][2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not ...
The absolute value (or modulus) of z may be thought of as the distance of P from the origin of that space. The formula for the absolute value of z = a + bi is similar to that for the Euclidean norm of a vector in a 2-dimensional Euclidean space : [ 5 ]
Since y is real, the absolute value of cos(y) + i sin(y) is necessarily 1. Therefore, the absolute value of e z can be 1 only if e x is 1; since x is real, that happens only if x = 0. Therefore z is purely imaginary and cos(y) + i sin(y) = 1. Since y is real, that happens only if cos(y) = 1 and sin(y) = 0, so that y is an integer multiple of 2 ...