B Understanding the Differences between Quartiles and Percentiles

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The discussion focuses on calculating the first quartile (Q1) of a set of 18 scores using two methods: a formulaic approach and a logical approach. The formulaic method yields Q1 as 3.75, while the logical method identifies Q1 as the median of the lower half of the data, resulting in a value of 4. There is no universally accepted "correct" method, as both approaches can be valid depending on the context. The conversation also touches on the need to refer to specific educational standards, such as the Australian NSW syllabus, for clarity on expectations. Understanding these differences is crucial for accurate statistical analysis and education.
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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
 
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pbuk said:
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.
 
YouAreAwesome said:
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!
 
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