Titel_SS06

e.g. the 0.65 quantile of a given data set of observations is the observation for which 65% of
all observations in the data set have smaller values. The 0.75 quantile is also denoted the
upper quartile (see also the Tukey box plots in the next section) while the 0.25 quantile is
denoted the lower quartile. The median thus equals the 0.5 quantile.

In order to construct a quantile plot the observations in the data set are arranged in ascending
order. The observation xiO in the ordered data set corresponding to the quantile can be
determined by:

Qi

i 1

i

Q

n



(2.19)

As an example consider the concrete cube compressive strength data from Table 2.2. These
are plotted in Figure 2.6, against the respective quantile values, see also Table 2.5. It can be
seen that the quantile plot has an almost constant slope over the whole range of observations.

From Table 2.5 it can be seen that no observation corresponds directly to the median of the
data set. In general the evaluation of a quantile which does not correspond to a given
observation must be based on an interpolation.

i xOi

Ordered

Qi

Table 2.5: Quantile values of the observed concrete cube compressive strength [MPa].