Inequalities why does $n<x<n$ include the numbers at both ends?

Question

So (high-school-level lower set maths tutor here!) if you have a grouped set of data such as $5 < t ≤ 10$, why is $7.5$ the midpoint? I'm puzzled because this midpoint - effectively the median - value ($7.5$) assumes values of t in the set to be $5,6,7,8, 9$ and $10$ right? But why is the $5$ included, if are values are supposed to be more than $5$? is it because one of the values could in theory be $5.0000001$ or whatever (ie, a tiny bit more than $5$? This is a similar dilemma that I had when I was looking at a question such as "what's the greatest possible weight of a $15$kg sack of potatoes whose weight has been rounded to the nearest kg. The correct answer is $15.5$, because, even though that would normally round to 16kg, we're thinking about a hypothetical sack of potatoes that's actually $15.49999...$(recurring), which would be then less than $15.5$. I may have answered my own question already (that is why is $7.5$ the midpoint of that grouped data interval?).