Quantiles and Percentiles

The $/alpha$-quantile $Q_{/alpha}$ is defined by the value where at least a portion $/alpha$ of the data is smaller and at least a portion 1-$/alpha$ larger. If the portions are given in percent then we speak about an $/alpha$-percentile $P_{/alpha}$. E.g. the 10%-percentile of the distribution of porosity in sandstone in the example on page (Table 2.2) is 21.4%. .25- und .75-quantiles are also called quartiles. The .5-quantile is equivalent to the median. Investigate how easy it is to find approximate quantiles from cumulative frequency polygons.