Why are there only 3 quartiles when dividing data into 4 equal parts?

[15123]

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%)?

 

[HallsofIvy]

That has nothing to do with probability or statistics but simple arithmetic. If you divide a rope or a stick into "n" pieces you will have to make "n-1" cuts.

 

[15123]

There is still a fourth quartile. If a score on a test is 22%, I put it in the first quartile, if the score is 33%, I put it under the Median and if the score is 70%, I put it under the third quartile. What do you do with a value that is 95%? You should put it in the fourth quartile, so to me there is a fourth quartile. My professor says there are only three quartiles.

I am still lost on this.

 

[mathman]

There seems to be a confusion between the number of intervals (4) and the number of cuts (3). It sounds to me that the professor is confused or you didn't understand him.

 

[15123]

There seems to be a confusion between the number of intervals (4) and the number of cuts (3). It sounds to me that the professor is confused or you didn't understand him.

I probably didn't understand him. I think he simply meant cuts=intervals-1.

 

[alan2]

A quartile, or any quantile for that matter, is a number, not an interval. The 25th quartile is the single value which 25% of the data falls below. It is not the interval, it is the cut. There certainly is an interval containing the largest 25% of data but that is not, by definition, a quartile. You are confusing intervals with their endpoints.

 

[15123]

A quartile, or any quantile for that matter, is a number, not an interval. The 25th quartile is the single value which 25% of the data falls below. It is not the interval, it is the cut. There certainly is an interval containing the largest 25% of data but that is not, by definition, a quartile. You are confusing intervals with their endpoints.

25th quartile? Don't you mean quantile? However, thanks for the explanation. Someone mentioned this to me, but I think he is incorrect:

Q1 - the lower 25% of the total probability

Q2 - the area encompassing 25%-75% of the total probability - Q2 is actually an area of 50% probability centered at the median.

Q3 - the area from 75%-100% of the total probability.

 

[alan2]

No, I meant quartile because you referred to 25%. It's just terminology but median, tercile, quartile, quintile, and percentile are special names for the quantiles that divide your interval into 2, 3, 4, 5, and 100 sub-intervals respectively. Whoever mentioned that quote to you was incorrect but I think you've got it now.