2.2.4.1 - Skewness & Central Tendency

The preferred measure of central tendency often depends on the shape of the distribution. In a symmetrical distribution, the mean, median, and mode are all equal. In these cases, the mean is often the preferred measure of central tendency. 

Symmetrical: Mean = Median = Mode

For distributions that are strongly skewed or have outliers, the median is often the most appropriate measure of central tendency because in skewed distributions the mean is pulled out toward the tail. The median is more resistant to outliers compared to the mean. Of these three measures of central tendency, the mean is most influenced by outliers. Below you will see how the direction of skewness impacts the order of the mean, median, and mode.

Skewed to the left: Mean < Median < Mode

Skewed to the right: Mode < Median < Mean