I have the following formula in my lecture notes for calculating the $j^{th}$ quartile in an interval:
$$Q_j=L_l+I\frac{N \frac{j}{4}-F_l}{f_l}, j=1,2,3$$
Where $L_l$ is the left side of the interval in which the quartile is. The interval in which the quartile is, is defined as the interval before the sum of the frequencies is bellow $N\frac{j}{4}$.
$F_l$ is the sum of the frequencies in the intervals before $L_l$
$f_l$ is the frequency in the interval of the median
- I is the length of the interval which contains the median
My question is:
If this formula is correct, how do I calculate the second quartile which is the median, when the formula is actually using information about the median ($f_l$ is the frequency in the interval of the median)?
Also, what is the intuition behind this formula (if it's correct of course)?