Understanding the Differences between Quartiles and Percentiles

[YouAreAwesome]

TL;DR Summary

Which way of calculating Q1 is correct, by formula or by logic?

Set of 18 scores = [2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]

Find Q1 by formula
Q1 is the (n+1)/4 th term (where n is the number of scores)
Q1 is the 19/4 th term, or the 4.75 th score.
Q1 is 0.75 of the way between scores 3 and 4 (the 4th and 5th scores in the set).
Q1=3.75
See https://www.hackmath.net/en/calculator/quartile-q1-q3

Find Q1 by logic
Q1 is the median of the "lower set" of scores - that is, if we split the scores into two equal sets at the median, the median of the lower of these is Q1.
The median of the of the Set provided above is 6.
The median of the lower Set provided above is 4.
See https://www.calculatorsoup.com/calculators/statistics/quartile-calculator.php

My question is, which of these methods is correct? And if both are correct but for different purposes, what are those purposes?

Thanks
YAA

 

[pbuk]

There is no agreed "correct" answer. This is covered reasonably well on Wikipedia https://en.wikipedia.org/wiki/Quartile#Computing_methods.

 

[YouAreAwesome]

There is no agreed "correct" answer. This is covered reasonably well on Wikipedia https://en.wikipedia.org/wiki/Quartile#Computing_methods.

Thanks. Now I have to go looking for what the Australian, NSW syllabus specifically wants from its students I suppose.

 

[PeroK]

Thanks. Now I have to go looking for what the Australian, NSW syllabus specifically wants from its students I suppose.

You could ask them about percentiles for a small sample while you're at it!