How should I calculate quartiles? In a book I read (by Amir D. Aczel) it is said that:
First quartile is th 25th percentile, that means a value for which $1/4$ of oberervation's results are lower.
Shouldn't it be
lower or equal? According to the book if I have observation like this:
$1, 3, 7, 9, 10, 11$
the value of the first quartile is on position: $(6+1)\cdot 0.25 = 1.75$, so it's $1.75$. But shouldn't it be $3$? For both $1.75$ and $3$ 25% of observations are below the given value. But that's the same for $1.25, 2.9$ and $2$. Are all answers correct?