50% are less intelligent than the median- the average (mean) can be different from the median.
If you have 10,20,20,20,50,80,100,100, the average is 50 and the median is 35, so half are higher than 35 and half lower.
However, in a normally distributed population, the mean (average), the median, and the mode are the same value.
BTW, when I think of nooses, I associate them with "Hang 'Em High", "The Oxbow Incident", and "Judgment at Nuremberg".