My professor stated the following: "Dividing in pieces is called 'quantiles'. In almost all cases quartiles are used, where n=4. We divide it into four equal pieces and we are going to check where the margin values are. Pay close attention: if I split my data into 4 equal pieces, I will have 3 quartiles. If I have 10 equal pieces, I have 9 deciles. You always have one less quantile than the n parts." I don't understand why there are always n-1 quantiles. Why is the 4th quartile never mentioned, not even in boxplots? Some people say this is because the 4th quartile is the supremum (<=100). So why does he say there are only 3 quartiles, when you have a 4th quartile as well? e.g.: if a student scores 95%, he will belong in the 4th quartile because I cannot classify him in the 3rd quartile (75%), because 95% is between 75% and 100% (75<95<100). If a quartile is 25%, then why do we only have 3 quartiles (3*25%=75%. What about the remaining 25%)?