Depending on the shape of the distribution, there exist some predictable relationships between the three measures of central tendency. In a perfectly symmetric distribution, the median and mean will have the exact same value.
If a symmetric distribution is unimodal, then the mode will also be equal to the median and mean.
Quite often, however, a distribution will exhibit some degree of skewness. Remember that the mean is a measure of centrality that is strongly affected by the extreme scores in the dataset. For this reason, the mean tends to be 'pulled towards' the tail-end of a skewed distribution.
For continuous data, the following guidelines are likely to hold for skewed distributions:
- In a positively skewed distribution, the mean is larger than the median, and both of these measures are larger than the mode:
- In a negatively skewed distribution, the opposite relationship holds; the mean is smaller than the median, and both these measures are smaller than the mode:
It should be noted that these guidelines for skewed data tend not to hold for discrete data.