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 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

1. The 0.7th quantile could equivalently be expressed as the... 70% quantile 70th quantile 0.7th percentile median
2. The 0.2th quantile could equivalently be expressed as the... 20th percentile 2nd percentile 0.2th percentile 20% percentile
3. The 0.5th quantile could equivalently be expressed as the... 5th percentile median 50th quantile 0.5th percentile

1. 70% quantile
2. 20th percentile
3. 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

Venables, W. N., and B. D. Ripley. 1999. Modern Applied Statistics with s-Plus. 3rd ed. New York: Springer-Verlag.

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These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND