- #1

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- 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]

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

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

**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