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A weighted average is an average that has multiplying factors to give different weights to data at different positions in the sample window. Mathematically, the weighted moving average is the convolution of the data with a fixed weighting function. One application is removing pixelization from a digital graphical image. [citation needed]
A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. If the random variable is denoted by X {\displaystyle X} , then the mean is also known as the expected value of X {\displaystyle X} (denoted E ( X ) {\displaystyle E(X)} ).
A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value." [2] [3]
Cumulative frequency distribution, adapted cumulative probability distribution, and confidence intervals. Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called frequency of non-exceedance.
In statistics, the mode is the value that appears most often in a set of data values. [1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmax x i P(X = x i)).
For a symmetric distribution with zero mean, the population MAD is the 75th percentile of the distribution. Unlike the variance, which may be infinite or undefined, the population MAD is always a finite number. For example, the standard Cauchy distribution has undefined variance, but its MAD is 1.
The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform.