**Quantitative Methods: Basic Concepts**

**Reading 7. Statistical Concepts and Market Returns**

**Learning Outcome Statements**

f. calculate and interpret quartiles, quintiles, deciles, and percentiles;

*CFA Curriculum, 2020, Volume 1*

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### Subject 5. Quartiles, Quintiles, Deciles, and Percentiles

**Quartile**

There are 3 quartiles in a data set. Between them, they divide the data into 4 equal parts or quarters. The first quartile is called the lower quartile and is often denoted as Q

_{1}. The second quartile is obviously just the median, as it is the middle value of the data set. The third quartile is called the upper quartile and is often denoted as Q

_{3}.

You should note that Q

_{1}effectively splits the data set into the lower 25% of values and the upper 75% of values whereas Q

_{3}splits the data into the lower 75% of values and the upper 25% of values.

The distance between Q

_{1}and Q

_{3}, namely Q

_{3}- Q

_{1}, is called the

**inter-quartile range**; it gives an indication of the spread of the middle 50% of the data set.

**Quintile**

There are 4 quintiles in a data set. Between them, they divide the data into 5 equal parts or fifths. Quintiles are not very commonly used.

You should note that the first quintile effectively splits the data set into the lower 20% of values and the upper 80% of values; the second quintile splits the data set into the lower 40% of values and the upper 60% of values, and so on.

**Decile**

There are 9 deciles in the data set. Between them, they divide the data into 10 equal parts, or tenths.

Obviously, the fifth decile is the median, as it is the middle value in the data set. The third decile splits the data set into the lower 30% of values and the upper 70% of values, and so on.

**Percentile**

There are 99 percentiles in the data set. Between them, they divide the data into 100 equal parts, or hundredths.

The fiftieth percentile is the median, as it is the middle value in the data set. The sixty-third percentile divides the data set into the lower 63% of values and the upper 37% of values, and so on.

Note that the 75th percentile is also the same value as Q

_{3}, for example.

These types of values are used to rank investment performance, such as the performance of mutual funds.

In calculating these values, it is important to first order the data set, as we did with the median. Once this is done, it is necessary to find the position of the value that you are calculating, and then the value itself (the procedure is exactly the same as that for calculating the median).

###
**User Contributed Comments**
8

You need to log in first to add your comment. ###### clama

Remember the formula ....

(N + 1) * Y/100

###### itconcepts

just splitting hair - if there are only 3 quartiles in a data set (2nd one being the median, then there should only be 89 Precentiles - other made up of quintiles and deciles - hehe

###### tschorsch

there are not 3 quartiles because the 2nd one is the mean

the 'tiles are divider lines

thus, there are n-1 n-tiles

i.e. for quartiles, they are at 25%, 50% and 75%

for deciles they are at 10%, 20% .. 80%, 90%

###### Dohei

tschorsch you do mean median in the first line I assume?

###### Mosobalaje

Who has has a look at the CFA mock afternoon session. Here is what it says:

20. The following ten observations are a sample drawn from a normal population: 25, 20, 18, -5, 35, 21, -11, 8, 20, and 9. The fourth quintile (80th percentile) of the sample is closest to:

A. 8.0

B. 21.0

C. 24.2

Answer = B

?Statistical Concepts and Market Returns,? Richard A. Defusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA 2011 Modular Level I, Vol. 1, pp. 375-378 Study Session 2-7-f

Describe, calculate and interpret quartiles, quintiles, deciles, and percentiles.

Ranking the sample from smallest to largest, we have -11, -5, 8, 9, 18, 20, 20, 21, 25, and 35. The fourth quintile (80th percentile) is the eighth largest of these ordered numbers. The eighth largest number is 21.

WHY IS THE ANSWER B? They did not even use the formula!!!

###### jayj001

(N+1) * (Y/100)

e.g. what is the 25th percentile / quartile 1? from a 15 observations.

Therefore = (15+1) * (25/100) = the 4th observation

###### Vladimir25

hi all,

I still cannot find the right answer/explanation on the CFA mock question posted above by Mosobalaje (80th percentile of the sample). Whole chapter regarding quantiles is based on the formula (n+1) * y/100 and linear interpolation, and then suddenly they use some different approach to resolve this problem!?

What might be the explanation here is that sample is taken from normal distribution and number of observations is less than 30, so we should use t-score and create one-side confidence interval (upper limit only). Using this approach I end up with some number close to 18, and then 21 is indeed correct answer, but I don't know if this is correct approach at all.

Any thoughts?

###### 8937558

Silly question: is there a way to sort data in ascending order using the Texas Instruments BAII calculator?