This note displays an interesting phenomenon for percentiles of independent
but non-identical random variables. Let $X_1,\cdots,X_n$ be independent random
variables obeying non-identical continuous distributions and $X^{(1)}\geq
\cdots\geq X^{(n)}$ be the corresponding order statistics. For any $p\in(0,1)$,
we investigate the $100(1-p)$%-th percentile $X^{(pn)}$ and prove
non-asymptotic bounds for $X^{(pn)}$. In particular, for a wide class of
distributions, we discover an intriguing connection between their median and
the harmonic mean of the associated standard deviations. For example, if
$X_k\sim\mathcal{N}(0,\sigma_k^2)$ for $k=1,\cdots,n$ and $p=\frac{1}{2}$, we
show that its median $\big|{\rm Med}\big(X_1,\cdots,X_n\big)\big|=
O_P\Big(n^{1/2}\cdot\big(\sum_{k=1}^n\sigma_k^{-1}\big)^{-1}\Big)$ as long as
$\{\sigma_k\}_{k=1}^n$ satisfy certain mild non-dispersion property.