2

I didn't find a definition for the upper median (or lower), but my guess would be the following:

If you have $2n$ samples for $n \in \mathbb{N}$ and $x_i$ is the i-th lowest value, the lower median is element $x_{n}$, the upper median is $x_{n+1}$ and the "normal" median is $\frac{x_{n}+x_{n+1}}{2}$

Is this correct?

Moritz Groß
  • 121
  • 5
  • 2
    Can you explain where you saw this? I would guess that it means the upper quartile which is the median of the upper half of the data. I never heard it called this before. Also, I have never heard of any names for the $x_n$ and $x_{n+1}$ that you are describing. – John L Mar 25 '21 at 14:03
  • 4
    @John L The "upper quartile" to which you refer has been called (by J. Tukey) the "upper hinge." Referring to it as a median would be inappropriate. Despite that, Googling indicates your guess is correct. It also indicates that primarily non-authoritative web sites (such as those devoted to helping schoolchildren) use that terminology! – whuber Mar 25 '21 at 14:12
  • 3
    @whuber would it be fair to say that these non-authoritative websites were authored by co-medians? – Sycorax Mar 25 '21 at 15:40
  • Or 'mediocrites' – BruceET Mar 25 '21 at 16:14
  • @Sycorax: NO, you cannot: COmedian is also a technical concept: https://stats.stackexchange.com/questions/165262/generalisation-of-the-notion-of-correlation-for-alpha-stable-distributions/165264#165264 – kjetil b halvorsen Mar 25 '21 at 16:34

0 Answers0