Comparing Measures of Central Tendency
Prerequisites
Percentiles,
Distributions, What
is Central Tendency, Measures of Central
Tendency, Mean and Median
Learning Objectives
 Compute the trimean
 Compute the geometric mean directly
 Compute the geometric mean using logs
 Use the geometric to compute annual portfolio returns
 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.
