$a,b,c,d,e$ are positive real numbers such that $a+b+c+d+e=8$ and $a^2+b^2+c^2+d^2+e^2=16$, find the range of $e$. 
$a,b,c,d,e$ are positive real numbers such that $a+b+c+d+e=8$ and $a^2+b^2+c^2+d^2+e^2=16$, find the range of $e$.

My book tells me to use tchebycheff's inequality
$$\left(\frac{a+b+c+d}{4}\right)^2\le \frac{a^2+b^2+c^2+d^2}{4}$$
But this not the Chebyshev's inequality given in wikipedia. Can someone state the actual name of the inequality so I can read more about it?
(I got $e\in\left[0,\frac{16}{5}\right]$ using the inequality)

The book means the special case $x=y$, $n=4$ of the Chebyshev inequality $\overline{xy} \geq \bar{x} \bar{y}$ where $x,y$ are sequences of length $n$, both arranged in the same order (such as both increasing or both decreasing), and the bar means averaging.  
