How to answer probability question with basic std dev statistics

Question

I have a data sample, say: $69$, $72$, $100$, $87$, $57$, $123$, $110$.

Knowing the standard deviation and the mean what is the answer to the question:

What is the number ($x$) for which $n\%$ out of all numbers of the sample are equal or greater than $x$?

For $n=60$ the question will be: What is the number ($x$) for which $60\%$ out of all numbers of the sample are equal or greater than $x$?

Thanks!

Answer 1

Well the data set you gave isn't a continuous one - there are a finite number of elements (specifically, seven of them).

There is no fraction with denominator $7$ that equals $0.6$, so there isn't an $x \in \mathbb{R}$ such that $60\%$ of the elements of $\{69, 72, 100, 87, 57, 123, 110\}$.

I'm sorry if this isn't the question you meant to ask, but the way you worded it, there isn't a solution.