I know that if I calculate the median, I am going to get a number that represents central tendency even if there are outliers that would cause the distribution to be skewed right or left. According to the Aerd Statistics website:
When you have a normally distributed sample you can legitimately use both the mean or the median as your measure of central tendency. In fact, in any symmetrical distribution the mean, median and mode are equal.
To me, it seems like median is clearly useful in situations where there is skewed distribution. But mean seems to be a useless measurement since in symmetrical distribution it will be almost identical to the median.
My question is: why is mean used at all when in the case of symmetrical distribution a median represents central tendency just as well?