§ Mean, Median and Jensen's
The intuition for Jensen's is typically presented as:
| \ /
| \ * /
| \ /
* is the average of the
@ is the of average of the x's.
- I wish to reinterpret this: the
@ is at the median of the s. So Jensen is maybe saying that the value at the median is lower than the mean of the values in this case due to the convexity of .
- In some sense, this tells us that the "data" is skewed in such a way that median is lower than the mean.
- I don't know if this perspective helps, or even if it is correct, but I wish to dwell on this perspective since it's one I don't use often. I've been thinking more along these lines due to competitive programming, and I quite enjoy the change!