Comparing Measures of Central Tendency

Prerequisites
Percentiles, Distributions, What is Central Tendency, Measures of Central Tendency, Mean and Median

Learning Objectives
  1. Compute the trimean
  2. Compute the geometric mean directly
  3. Compute the geometric mean using logs
  4. Use the geometric to compute annual portfolio returns
  5. Compute a trimmed mean

How do the various measures of central tendency compare with each other? For symmetric distributions, the mean, median, trimean, and trimmed mean are equal, as is the mode except in bimodal distributions. Differences among the measures occur with skewed distributions.

With a positively skewed distribution, the mean is typically higher than the median and the trimean and trimmed mean will fall between them. The geometric mean is usually lower than all measures except the mode.