Timeline for When is the function of a median closer to the median of the function than the mean of the function is to the function of the mean?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2011 at 6:00 | comment | added | Anthony Quas | @David: Maybe this helps: the average of $f(X)$ takes into account all the values of $f(X)$ and takes the midpoint of them; whereas $f$ applied to the average of $X$ depends only on the value of $f$ at one point. If the function isn't monotone, the value of $f$ at one point tells you very little about the value of $f$ at all the other points. | |
| Jan 31, 2011 at 2:20 | vote | accept | David LeBauer | ||
| Jan 31, 2011 at 2:20 | history | bounty ended | David LeBauer | ||
| Jan 31, 2011 at 2:20 | comment | added | David LeBauer | @Anthony Thanks for the answer; I was hoping to find something useful to say about seriously non-monotone f, but equally interested that such something does not exist. | |
| Jan 25, 2011 at 20:03 | history | edited | Anthony Quas | CC BY-SA 2.5 |
grammar fix
|
| Jan 25, 2011 at 9:45 | comment | added | Did | Anthony: Nice post. I wonder what would be quantitative versions of the result you mention for functions that are close to a linear function and of the result you mention for nearly monotone functions. | |
| Jan 25, 2011 at 9:28 | history | edited | Anthony Quas | CC BY-SA 2.5 |
added 462 characters in body
|
| Jan 25, 2011 at 9:18 | history | answered | Anthony Quas | CC BY-SA 2.5 |