In reply to Carlos Castillo.

I think you misread the article. I did not claim that the median is approximately (1-x)^3. What I said is that the median of a chi-sq(d) distribution is approximately d(1-2/(9d))^3 when d > 0.125. I also said that the median is approximately d - 2/3 for sufficiently large values of d. "Sufficiently large" means that d >> 2/9 (which is read "much much greater than 2/9"). Empirically, d > 1 is probably good enough.

Regarding citation, you can cite this blog as
Wicklin, Rick (2011) "On the median of the chi-square distribution," published in The DO Loop blog, 09NOV2011.
URL: https://blogs.sas.com/content/iml/2011/11/09/on-the-median-of-the-chi-square-distribution.html