## 1.4 Some other useful summary statistics

### 1.4.1 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**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
- median

### 1.4.2 Minimum and Maximum

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.

### References

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