Quartiles and quarters

[Harry_the_cat]

Suppose you have 10 pieces of data: a, b, c, d, e, f, g, h, i, j arranged in ascending order.
The median is (e+f)/2. The lower quartile is c and the upper quartile is h.
Does the upper QUARTER include h or omit it. That is, is the upper quarter {h, i, j} or {i, j}? Is this defined anywhere?

 

[Dr.Peterson]

I don't know that "upper quarter" is a defined term at all. How do you use it?

But even the quartiles themselves are not clearly defined. Various textbooks and statistics software give different methods that yield different answers. Here is one source showing a large variety of methods: Quartiles in Elementary Statistics, Langford

For five of these methods, see https://mathworld.wolfram.com/Quartile.html

For a long discussion of this, see my blog where I quote from a detailed answer to questions about this issue: The Many Meanings of “Quartile”