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This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). [1]
The Minkowski difference (also Minkowski subtraction, Minkowski decomposition, or geometric difference) [1] is the corresponding inverse, where () produces a set that could be summed with B to recover A. This is defined as the complement of the Minkowski sum of the complement of A with the reflection of B about the origin. [2]
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
The sum of squared deviations needed to calculate sample variance (before deciding whether to divide by n or n − 1) is most easily calculated as = From the two derived expectations above the expected value of this sum is
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
Replace numbers #1 and #2 by their difference; #3 and #4 by their difference; etc. Sort the list of n/2 differences from large to small. Assign each pair in turn to different sets: the largest in the pair to the set with the smallest sum, and the smallest in the pair to the set with the largest sum.
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of z 2 + 4 {\displaystyle z^{2}+4} can be found using difference of two squares:
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.