A quantile is the point at which a certain percentage of the data falls below a certain value. For example, recall the
Height variable from the
survey data set which contains the responses of Statistics students to a set of questions (Venables and Ripley 1999).
Suppose we wanted to know what height a student would need to be to be in the shortest 10% of the sample. It turns out that students whose height is less than 160cm are among the shortest 10% of the sample. We can therefore say that 160cm is the 0.1th quantile, or equivalently, the 10% quantile, or the 10th percentile. The 50% quantile, or the 50th percentile, is in fact the median.
This video explains more about quantiles and percentiles.
Test your knowledge
- The 0.7th quantile could equivalently be expressed as the...
- The 0.2th quantile could equivalently be expressed as the...
- The 0.5th quantile could equivalently be expressed as the...
- 70% quantile
- 20th percentile
The minimum and maximum values are also useful pieces of information for us to know and, like the median, are most easily determined by first listing the data in order from smallest to largest. Consider again the \(n=5\) income values we considered earlier, listed in order as \[1170, 1740, 6940, 25000, 66300.\]
The minimum and maximum values are then 1170 and 66300 respectively.