Titel_SS06

Quantile value

Concrete cube compressive strength [MPa]

Figure 2.6: Quantile plots of the observed concrete cube compressive strength.

Tukey Box Plots

Tukey box plots provide information about several sample characteristics of the observations
contained in a data set, see Figure 2.7.

The median is typically represented by a circle or a horizontal line within the box. The upper
and lower sides of the box indicate the values of the upper and the lower quartiles,
respectively. The distance between these quartiles is called the interquartile range, ; 50% of
the data are located within this range. A large interquartile range indicates that the
observations are widely dispersed around the median and vice versa.

r

Another feature of the Tukey box plot is the so called adjacent values. The upper adjacent
value is defined as the largest observation less than or equal to the upper quartile plus 1.5.
The lower adjacent value is defined as the smallest observation greater than or equal to the
lower quartile minus 1.5. If an observation has a value outside the adjacent values, the
observation is called an outside value and is shown in the box plot by a single point.

r

r

Outside values
Upper adjacent value:
largest value less than
0.75 quantile + 1.5 r

Upper quartile value

Median

Lower quartile value

Lower adjacent value:

lowest value larger than

Outside value 0.25 quantile - 1.5 r

Data values

r : Interquartile range (50% of data)

r

Figure 2.7: Tukey box plot with indication of the characteristics of the data set.

In Figure 2.8 the Tukey box plot for the concrete cube compressive strength data is given