Name Equation or description As solution to optimization problem Arithmetic mean Median A middle value that separates the higher half from the lower half of the data set; may not be unique if the data set contains an even number of points Geometric median A rotation invariant extension of the median for points in Tukey median Another rotation invariant extension of the median for points in —a point that maximizes the Tukey depth Mode The most frequent value in the data set Geometric mean Harmonic mean Contraharmonic mean Lehmer mean Quadratic mean(or RMS) Cubic mean Generalized mean Quasi-arithmetic mean is monotonic Weighted mean Truncated mean The arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded Interquartile mean A special case of the truncated mean, using the interquartile range. A special case of the inter-quantile truncated mean, which operates on quantiles (often deciles or percentiles) that are equidistant but on opposite sides of the median. Midrange Winsorized mean Similar to the truncated mean, but, rather than deleting the extreme values, they are set equal to the largest and smallest values that remain Medoid A representative object of a set of objects with minimal sum of dissimilarities to all the objects in the set, according to some dissimilarity function .
Name Equation or description As solution to optimization problem Arithmetic mean Median A middle value that separates the higher half from the lower half of the data set; may not be unique if the data set contains an even number of points Geometric median A rotation invariant extension of the median for points in Tukey median Another rotation invariant extension of the median for points in —a point that maximizes the Tukey depth Mode The most frequent value in the data set Geometric mean Harmonic mean Contraharmonic mean Lehmer mean Quadratic mean(or RMS) Cubic mean Generalized mean Quasi-arithmetic mean is monotonic Weighted mean Truncated mean The arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded Interquartile mean A special case of the truncated mean, using the interquartile range A special case of the inter-quantile truncated mean, which operates on quantiles (often decile.s or percentiles) that are equidistant but on opposite sides of the median. Midrange Winsorized mean Similar to the truncated mean, but, rather than deleting the extreme values, they are set equal to the largest and smallest values that remain Medoid A representative object of a set of objects with minimal sum of dissimilarities to all the objects i,n the set according to some dissimilarity function .