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Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
In some circumstances, mathematicians may calculate a mean of an infinite (or even an uncountable) set of values. This can happen when calculating the mean value of a function (). Intuitively, a mean of a function can be thought of as calculating the area under a section of a curve, and then dividing by the length of that section.
Ideally, a new element would be created using the mean of the upper and lower weighted medians and assigned a weight of zero. This method is similar to finding the median of an even set. The new element would be a true median since the sum of the weights to either side of this partition point would be equal.
Average of chords. In ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list.
Taking the mean μ of X to be 0, the median of Y will be 1, independent of the standard deviation σ of X. This is so because X has a symmetric distribution, so its median is also 0. The transformation from X to Y is monotonic, and so we find the median e 0 = 1 for Y. When X has standard deviation σ = 0.25, the distribution of Y is weakly skewed.
The median is computed in each single dimension in the Manhattan-distance formulation of the k-medians problem, so the individual attributes will come from the dataset (or be an average of two values from the dataset).
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f ( x ) over the interval ( a , b ) is defined by: [ 1 ]
Mean shift is a non-parametric feature-space mathematical analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm. [1] Application domains include cluster analysis in computer vision and image processing .