Interpretation of a problem involving Chebyshev's inequality

Question

I found the next problem, I know that I will use the Chebyshev's inequality but I don't understand the "question" of the problem

Precisely, I don't understand the phrase "...fraction of $x_1,\ldots,x_n$ included in the interval...". What does it mean?

I'm not looking for a solution of the problem (well yes, but is not the point of my question), I'm trying to understand the problem.

The problem is from Statistical Inference by V.K Rohatgi (3.7.28).

Answer 1

In general

the fraction of $x_1,\ldots,x_n$ included in set $A$

means

the proportion of elements of the list $x_1, \ldots, x_n$ that lie in the set $A$

This is calculated as the number of elements that lie in set $A$, divided by $n$: $$\frac{ \#\{i: x_i \in A\}}n.$$

As a hint to the solution to your problem: To apply Chebyshev's inequality, you need a random variable $X$.

Let $X$ be an element chosen uniformly at random from the list $x_1,\ldots, x_n$.