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Probability density functions (pdfs) and probability mass functions are denoted by lowercase letters, e.g. , or . Cumulative distribution functions (cdfs) are denoted by uppercase letters, e.g. , or . In particular, the pdf of the standard normal distribution is denoted by , and its cdf by .
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
Plus–minus sign. The plus–minus sign or plus-or-minus sign, ±, is a symbol with multiple meanings. In mathematics, it generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction. In statistics and experimental sciences, the sign commonly indicates the confidence ...
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. [1][2]
Example of samples from two populations with the same mean but different standard deviations. Red population has mean 100 and SD 10; blue population has mean 100 and SD 50. A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
Arithmetic mean. In mathematics and statistics, the arithmetic mean ( / ˌærɪθˈmɛtɪk / arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. [1] The collection is often a set of results from an experiment, an ...
Definition. The p -value is the probability under the null hypothesis of obtaining a real-valued test statistic at least as extreme as the one obtained. Consider an observed test-statistic from unknown distribution . Then the p -value is what the prior probability would be of observing a test-statistic value at least as "extreme" as if null ...
Mean. A mean is a numeric quantity representing the "center" of a collection of numbers or the number that you can replace all the numbers in a data set by to still achieve the same total (the total is not necessarily the sum). [1] There are several kinds of means (or "measures of central tendency ") in mathematics, especially in statistics.