Question 390733
The 1st quartile Q1 demarcates the lowest 25% of the distribution from the higher 75%.
The 3rd quartile Q3 demarcates the lower 75% of the distribution from the highest 25%.
(We are assuming here that the values of the RV are either in increasing or decreasing order.)
What is in between the Q1 and Q3 then, is exactly 50% of the distribution. (Think of it this way: Exclude the lowest 25% of the distribution and the highest 25% of the distribution and you get exactly the middle 50% of the distribution.)