Given N measurements of the composition vector, we construct a D × N matrix, which contains observations of compositions, x N = [x 1 , x2 , ..., xD ], in which each xi is a column vector of the x i composition for that observation. We are most interested in the measure of central tendencycenter, ξ of the data, which is similar in interpretation to the mean of the data set in Euclidean statistics. The center of the data is given as