# mean vs median geometric interpretation?

I'm looking at this picture on wikipedia, comparing the median and mean of an arbitrary distribution. But what does it mean exactly? From the figure, it looks like the mean is the center of mass of the distribution (in the sense that you could balance the distribution on that point). However, since the median has $$50\%$$ to its left and right, it seems a more reasonable candidate for the center of mass. Which one is it? And what is the geometric interpretation of the other metric? • In a symmetric distribution, (normal, for example) the median is equal to the mean. Both measures are estimates of central tendency, but the mean is morr affected by extreme values and outliers than the median is. One can think of the mean as a "balancing point" ; if our distribution was an object, we could balance it on a fulcrum at the mean Nov 24, 2018 at 18:18
• @WaveX: but that's what i find weird. in the picture, it seems that the median has 50% of the mass on its left and 50% on its right. So, why does the object balance on the mean instead? Nov 24, 2018 at 18:20
• Perhaps this link may be able to explain it a little more Nov 24, 2018 at 18:56

The two sets $$\{1,2,3\}$$ and $$\{1,2,100\}$$ have the same median. But the second set's center of mass is at $$34$$.