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

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In summary, the conversation discusses the concept of quantiles and how they are used in data analysis. The speaker explains that when dividing data into equal parts, there will always be n-1 quantiles. There is some confusion about the number of intervals and cuts, but ultimately, a quartile is a single value representing the percentage of data falling below it. However, the conversation ends with a discussion about the terminology and how it can be confusing.
  • #1
15123
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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%)?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
mathman said:
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.
 
  • #6
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.
 
  • #7
alan2 said:
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:
someperson said:
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.
 
  • #8
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.
 

What are quantiles?

Quantiles are a statistical concept used to divide a dataset into equal-sized groups. They represent the values that divide the data into specific percentages or proportions.

How are quantiles different from percentiles?

Quantiles and percentiles are similar concepts, but they are calculated differently. While quantiles divide the data into equal-sized groups, percentiles divide the data into 100 equal-sized groups. So, quantiles divide the data into quarters (25%), quintiles (20%), or deciles (10%), while percentiles divide the data into 100ths (1%).

Why are quantiles important in statistics?

Quantiles are important because they provide a way to summarize and analyze large amounts of data. They can give insights into the distribution of the data and help identify outliers or extreme values. They are also used in various statistical methods, such as hypothesis testing and regression analysis.

What is the difference between quartiles and quantiles?

Quartiles are a type of quantile that divides the data into four equal-sized groups, while quantiles can divide the data into any number of equal-sized groups. Quartiles are specifically used to divide the data into four quarters, while quantiles can divide the data into any percentage or proportion.

How are quantiles calculated?

The most common method for calculating quantiles is the interpolation method, which involves finding the values that fall between two data points and calculating the average. For example, the first quartile (Q1) would be the average of the data point at the 25th percentile and the data point at the 26th percentile. There are also other methods, such as the nearest-rank method and the inverse cumulative distribution function method.

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