Quantiles

In statistics, quantiles are points that divide the range of a probability distribution into continuous intervals that have equal probabilities.

The common quantiles are:

• Quartiles (four equal portions of a distribution)
• Deciles (ten equal portions of a distribution)
• Percentiles (hundred equal portions of a distribution)

Let us take an example. If we divide a distribution into three equal portions, we will speak of three quartiles. The first quartile includes all values that are smaller than a quarter of all values. And, when data points are presented in ascending order, the lower quartile, or first quartile (Q1), is the value under which 25% of the data points are found.

Similarly, a percentile divides the distribution into 100 equal parts.

Take a look at the image of a quantiles distribution below.

In the image above, the median is showing that there are 50 equal portions of distribution and hence, it is the 50th percentile (half of a percentile). 

Also, the first quartile, under which 25% of the data points are found, is at the 25th percentile (one-fourth of hundredth percentile. Similarly, the third quartile, under which 75% of the data points are found, is at the 75th percentile (three fourth of hundredth percentile).

The largest value towards the right is showing the 100th percentile since the point shows all 100 values in the distribution.