Median is often better, but not always—it depends on the purpose you wish to put the data to. With anything less than the full distribution, you’ll be able to hit some cases in which it can mislead you.
Edited to add:
Specifically—if you are interested in totals, mean is usually a more useful “average”. Multiplying the total number of water balloons by the average amount of water in a balloon gives you a much better estimate (exact, in theory) with mean than with median. If you are interested in individuals, median is usually better; if I am asking if the next water balloon will have more than X amount of water, median is a much more informative number. Neither is going to well represent a multimodal distribution, which we might expect to be dealing with in the great*-grandparent’s case anyway if the hypothesis of a strong genetic component to variation in intelligence does in fact hold.
Median is often better, but not always—it depends on the purpose you wish to put the data to. With anything less than the full distribution, you’ll be able to hit some cases in which it can mislead you.
Edited to add:
Specifically—if you are interested in totals, mean is usually a more useful “average”. Multiplying the total number of water balloons by the average amount of water in a balloon gives you a much better estimate (exact, in theory) with mean than with median. If you are interested in individuals, median is usually better; if I am asking if the next water balloon will have more than X amount of water, median is a much more informative number. Neither is going to well represent a multimodal distribution, which we might expect to be dealing with in the great*-grandparent’s case anyway if the hypothesis of a strong genetic component to variation in intelligence does in fact hold.
Good point. You should select a metric that would be most useful in any given situation, be it the mean, the median, or anything else.