How can i explain Interval date in my stats class?

Answer 1

It depends on how you have your intervals set up. If all the intervals are equal, just use the arithmetic mean (the midpoint or average) for each interval.

But if you're spreading out your intervals geometrically, by log transformations, or by percentage increases (e.g., in 50% increments such as 10-15, 15-22, 22-33, 33-50, 50-75, etc), then I'd use the geometric mean to identify each interval. To get that, just multiply the ends of the interval together, then take the square root and round it off.

For that 50% example I gave, the intervals might be identified or clustered at sqrt(10x15) = 12; then 18, 27, 41, 61 ...

If you're going to do any analysis of grouped data, this is the way to go.

Answer 2

They're called interval data because the length of an interval matters.

For example, if Alice is 170 cm and Beth is 174 cm then it makes sense to say that the diference is 4 cm. In other words, the length of the interval [170;174]

Unlike data that are text strings, ordered alphabetically. You can say the "Alice"<"Beth" but you can't talk about the difference "Beth"-"Alice".

Actually I think it's a stupid term since you actually can talk about the interval ["Alice";"Beth"], namely the set of all text strings that come between. You just can't talk about the length of the interval.