The median of a list of numbers is the value that minimizes the sum of absolute differences to each value, sum([abs(median - x) for x in list])
The average of a list of numbers is the value that minimizes the sum of squared difference to each value, sum([squared(mean - x) for x in list])
They're both summary statistics in that they're single numbers used to describe a dataset, but a median is not a "kind of average." The mean is the mean and nothing else.
Incorrect, median, mean, and mode are all types of averages. Usually when people say average they mean the mean, but they're all different kinds of averages trying to identify the central tendency.
"Average: a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number." -- Google
> Incorrect, median, mean, and mode are all types of averages.
There's a bunch of means (arithmetic, geometric, and harmonic, for instance), and they are all (as well as median and mode) averages.
Though, usually when people say "mean" without further specifics they mean the "arithmetic mean", and usually when they say "average" without further specifics they also mean "arithmetic mean" (though "median" is also fairly common, and "mode" isn't that uncommon.)
Take [0,2,100]: average is 34, but median is 2.