Unimodal Distributions
The difference between the mean and the mode in a unimodal distribution is bounded by 31/2. In symbols
where || is the absolute value. Incidentally this formula is also the Pearson mode or first skewness coefficient, and shows that this statistic for a unimodal distribution is bounded by 31/2.
The difference between the mode and the median has the same bound. In symbols
Read more about this topic: Mode (statistics)