Quantiles
What are quantiles?
Quantiles are positional markers that divide a sorted distribution into equal parts.
What are they used for?
Quantiles offer information about the structure of a distribution, where values are arranged in either ascending or descending order.
Types of quantiles
There are various types of quantiles.
- Terziles
Terziles divide the distribution into 3 equal parts. - Quartiles
Quartiles divide the distribution into 4 equal parts. - Quintiles
Quintiles divide the distribution into 5 equal parts. - Deciles
Deciles divide the distribution into 10 equal parts. - Percentiles (or centiles)
Percentiles divide the distribution into 100 equal parts.
A practical example
Let’s take this distribution as an example:
$$ X = \{ 3, 10, 6, 4 , 1, 9, 8 , 2, 7, 5, 11 \} $$
When we sort it in ascending order, it becomes:
$$ X = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \} $$
The value that divides the distribution into two equal parts is called the median.
In this case, the median is x=6.
$$ X = \{ \underbrace{1, 2, 3, 4, 5}_{1}, \color{red}6, \underbrace{7, 8, 9, 10, 11}_{2} \} $$
The values that split the distribution into four equal parts are known as quartiles.
In this example, the quartiles are q1=3, q2=6, and q3=9.
$$ X = \{ \underbrace{1, 2}_{1}, \color{red}3, \underbrace{4, 5}_{2}, \color{red}6, \underbrace{7, 8}_{3}, \color{red}9, \underbrace{10, 11}_{4} \} $$
The terms q1, q2, and q3 are referred to as the first, second, and third quartiles, respectively.
Note: The second quartile (q2) always corresponds to the median.
And so on.
