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The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by <x>=sum_(i=1)^nw_ix_i, (1) where each weight w_i is a nonnegative ...

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are ...

The mean clustering coefficient of a graph G is the average of the local clustering coefficients of G. It is implemented in the Wolfram Language as ...

Let a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = (2a_nb_n)/(a_n+b_n). (2) Then A(a_0,b_0)=lim_(n->infty)a_n=lim_(n->infty)b_n=sqrt(a_0b_0), (3) which is just the geometric mean.

Let alpha_(n+1) = (2alpha_nbeta_n)/(alpha_n+beta_n) (1) beta_(n+1) = sqrt(alpha_nbeta_n), (2) then H(alpha_0,beta_0)=lim_(n->infty)a_n=1/(M(alpha_0^(-1),beta_0^(-1))), (3) ...

The mean tetrahedron volume V^_ is the average volume of a tetrahedron in tetrahedron picking within some given shape. As summarized in the following table, it is possible to ...

Let a function h:U->R be continuous on an open set U subset= C. Then h is said to have the epsilon_(z_0)-property if, for each z_0 in U, there exists an epsilon_(z_0)>0 such ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

The extended mean-value theorem (Anton 1984, pp. 543-544), also known as the Cauchy mean-value theorem (Anton 1984, pp. 543) and Cauchy's mean-value formula (Apostol 1967, p. ...