# Why use mean when you can use median?

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?

• If $X$ and $Y$ are random variables, is the median of $X+Y$ the sum of the medians of $X$ and $Y$? Oct 13, 2017 at 4:57
• Why do you think the mean is only useful if you have a symmetric distribution?
– bof
Oct 13, 2017 at 6:04
• Added reasoning for thinking mean is only useful in symmetric distribution. I'm not saying I'm correct. Just notifying everyone that I provided the quote that led me to ask the question I did. Oct 13, 2017 at 6:35