Chebyshev's inequality: "It is obvious ..."

Having trouble internalizing the last sentence from my textbook's snippets:

Quote:

For a binomially distributed random variable

, it can be shown, that the following holds:

**(16)**

I would like to understand it visually (e.g.: probability distribution graph, is at MAX., now look at the points, ...).(Happy)

BTW, I've also found

a similar thread, but could not work out the proof for

*Theorem 4* from

.pdf **mr fantastic** provided:

. Why does the

hold? (Thinking)

PS: Please, feel free to correct any grammatical mistake you find. (Nod)