## 1.4 Quantiles and Percentiles

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

*, or the*

**10% quantile***. The*

**10th percentile***, or the*

**50% quantile***, is in fact the*

**50th percentile***.*

**median****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
- 2nd percentile
- median

### References

Venables, W. N., and B. D. Ripley. 1999.

*Modern Applied Statistics with s-Plus*. 3rd ed. New York: Springer-Verlag.