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  2. 68–95–99.7 rule - Wikipedia

    en.wikipedia.org/wiki/68–95–99.7_rule

    In the social sciences, a result may be considered statistically significant if its confidence level is of the order of a two-sigma effect (95%), while in particle physics and astrophysics, there is a convention of requiring statistical significance of a five-sigma effect (99.99994% confidence) to qualify as a discovery.

  3. Standard deviation - Wikipedia

    en.wikipedia.org/wiki/Standard_deviation

    In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value ) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

  4. σ-algebra - Wikipedia

    en.wikipedia.org/wiki/Σ-algebra

    In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair (,) is called a measurable space.

  5. 97.5th percentile point - Wikipedia

    en.wikipedia.org/wiki/97.5th_percentile_point

    In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96, meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean.

  6. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function.

  7. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value

  8. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

  9. σ-finite measure - Wikipedia

    en.wikipedia.org/wiki/Σ-finite_measure

    In mathematics, a positive or a signed measure μ on a set X is called σ-finite if X equals the union of a sequence of measurable sets A 1, A 2, A 3, … of finite measure μ(A n) < ∞. Similarly, a subset of X is called σ-finite if it equals such a countable union.