Separating the observations into 1/4.
Q_1 = p25 Q_2 = p50 Q_3 = p75
Quintiles (5ths) and Deciles (10ths) are also common.
Combined with the minimum and maximum values, you get the “five-number summary” which is p0, p25, p50, p75, p100.
Interquartile range (IQR) is the difference between the 1st and 3rd quartiles. It represents 50% of the data and lets you know the spread.
IQR is also used to find upper and lower limits, called “fences”. This is to determine outliers.
lower limit = Q_1 - (1.5*IQR) upper limit = Q_3 + (1.5*IQR)
Any data points outside of those limits are “outliers”.
You can calculate the quartiles by first getting the median, then taking the median of each of the halves. If you split on a proper pivot point, I believe that we don’t include that when calculating median of the other sections.