Chapter 2 An example via quantiles

We will now consider the concept of probability in the context of some of the concepts we discussed in previous topics, namely histograms and quantiles. 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):

Also recall that 160cm is the 0.1th quantile; that is, that students whose height is less than 160cm are among the shortest 10% of the sample:

We could think about this through the lens of probability as follows. Suppose a student from this sample of students were randomly selected. What is the probability their height would be less than 160cm? The answer is 0.1. This is because 160cm is the 0.1th quantile.

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